Dissipative preparation of entanglement in optical cavities

Entangled dark state mediated by a dielectric cavity within epsilon-near-zero materials

Two emitters can be entangled by manipulating them through optical fields within a photonic cavity. However, maintaining entanglement for a long time is challenging due to the decoherence of the entangled qubits, primarily caused by cavity loss and atomic decay. Here, we found the entangled dark state between two emitters mediated by a dielectric cavity within epsilon-near-zero (ENZ) materials, ensuring entanglement maintenance over an extended period. To obtain the entangled dark state, we derived an effective model with degenerate mode modulation. In the dielectric cavities within ENZ materials, the decay rate of emitters can be regarded as 0, which is the key to achieving the entangled dark state. Meanwhile, the dark state immune to cavity loss exists when two emitters are in symmetric positions in the dielectric cavity. Additionally, by adjusting the emitters to specific asymmetric positions, it is possible to achieve transient entanglement with higher concurrence. By overcoming the decoherence of the entangled qubits, this study demonstrates stable, long-term entanglement with ENZ materials, holding significant importance for applications such as nanodevice design for quantum communication and quantum information processing.

Experimental Realization of Nonunitary Multiqubit Operations

We demonstrate a novel experimental tool set that enables irreversible multiqubit operations on a quantum platform. To exemplify our approach, we realize two elementary nonunitary operations: the or and nor gates. The electronic states of two trapped ^{40}Ca^{+} ions encode the logical information, and a cotrapped ^{88}Sr^{+} ion provides the irreversibility of the gate by a dissipation channel through sideband cooling. We measure 87% and 81% success rates for the or and nor gates, respectively. The presented methods are a stepping stone toward other nonunitary operations such as in quantum error correction and quantum machine learning.

Many-body cavity quantum electrodynamics with driven inhomogeneous emitters

Quantum emitters coupled to optical resonators are quintessential systems for exploring fundamental phenomena in cavity quantum electrodynamics (cQED)¹ and are commonly used in quantum devices acting as qubits, memories and transducers². Many previous experimental cQED studies have focused on regimes in which a small number of identical emitters interact with a weak external drive^3-6, such that the system can be described with simple, effective models. However, the dynamics of a disordered, many-body quantum system subject to a strong drive have not been fully explored, despite its importance and potential in quantum applications^7-10. Here we study how a large, inhomogeneously broadened ensemble of solid-state emitters coupled with high cooperativity to a nanophotonic resonator behaves under strong excitation. We discover a sharp, collectively induced transparency (CIT) in the cavity reflection spectrum, resulting from quantum interference and collective response induced by the interplay between driven inhomogeneous emitters and cavity photons. Furthermore, coherent excitation within the CIT window leads to highly nonlinear optical emission, spanning from fast superradiance to slow subradiance¹¹. These phenomena in the many-body cQED regime enable new mechanisms for achieving slow light¹² and frequency referencing, pave a way towards solid-state superradiant lasers¹³ and inform the development of ensemble-based quantum interconnects^9,10.

Cooling neutral atoms into maximal entanglement in the Rydberg blockade regime

We propose a cooling scheme to prepare stationary entanglement of neutral atoms in the Rydberg blockade regime by the combination of periodically collective laser pumping and dissipation. In each cycle, the controlled unitary dynamics process can selectively pump atoms away from the nontarget state while keeping the target state unchanged. The subsequent dissipative process redistributes the populations of ground states through the engineered spontaneous emission. After a number of cycles, the system will eventually be stabilized into the desired steady state, independent of the initial state. This protocol does not rely on coherent addressing of individual neutral atoms or fine control of Rydberg interaction intensity, which can, in principle, greatly improve the feasibility of experiments in related fields.

Efficient Source of Shaped Single Photons Based on an Integrated Diamond Nanophotonic System

An efficient, scalable source of shaped single photons that can be directly integrated with optical fiber networks and quantum memories is at the heart of many protocols in quantum information science. We demonstrate a deterministic source of arbitrarily temporally shaped single-photon pulses with high efficiency [detection efficiency=14.9%] and purity [g^{(2)}(0)=0.0168] and streams of up to 11 consecutively detected single photons using a silicon-vacancy center in a highly directional fiber-integrated diamond nanophotonic cavity. Combined with previously demonstrated spin-photon entangling gates, this system enables on-demand generation of streams of correlated photons such as cluster states and could be used as a resource for robust transmission and processing of quantum information.

Resource-Efficient Dissipative Entanglement of Two Trapped-Ion Qubits

We demonstrate a simplified method for dissipative generation of an entangled state of two trapped-ion qubits. Our implementation produces its target state faster and with higher fidelity than previous demonstrations of dissipative entanglement generation and eliminates the need for auxiliary ions. The entangled singlet state is generated in ∼7  ms with a fidelity of 0.949(4). The dominant source of infidelity is photon scattering. We discuss this error source and strategies for its mitigation.

Generation of a Maximally Entangled State Using Collective Optical Pumping

We propose and implement a novel scheme for dissipatively pumping two qubits into a singlet Bell state. The method relies on a process of collective optical pumping to an excited level, to which all states apart from the singlet are coupled. We apply the method to deterministically entangle two trapped ^{40}Ca^{+} ions. Within 16 pumping cycles, an initially separable state is transformed into one with 83(1)% singlet fidelity, and states with initial fidelity of ⪆70% converge onto a fidelity of 93(1)%. We theoretically analyze the performance and error susceptibility of the scheme and find it to be insensitive to a large class of experimentally relevant noise sources.

Dissipative preparation of qutrit entanglement via periodically modulated Rydberg double antiblockade

We propose a mechanism of Rydberg double antiblockade by virtue of a resonant dipole-dipole interaction between a pair of Rydberg atoms placed at short distances scaling as 1/R³. By combining this novel excitation regime with microwave-driven fields and dissipative dynamics, a stationary qutrit entangled state can be obtained with high quality, the corresponding steady-state fidelity and purity are insensitive to the variations of the dynamical parameters. Furthermore, we introduce time-dependent laser fields with periodically modulated amplitude to speed up the entanglement creation process. Numerical simulations reveal that the order of magnitude of the shortened convergence time is about 10³ in units of ω₀, and the acceleration effect appears valid in broad parametric space. The present results enrich the physics of the Rydberg antiblockade regimes and may receive more attention for the experimental investigations in dissipative dynamics of neutral atoms.

Entanglement Entropy Scaling Transition under Competing Monitoring Protocols

Dissipation generally leads to the decoherence of a quantum state. In contrast, numerous recent proposals have illustrated that dissipation can also be tailored to stabilize many-body entangled quantum states. While the focus of these works has been primarily on engineering the nonequilibrium steady state, we investigate the buildup of entanglement in the quantum trajectories. Specifically, we analyze the competition between two different dissipation channels arising from two incompatible continuous monitoring protocols. The first protocol locks the phase of neighboring sites upon registering a quantum jump, thereby generating a long-range entanglement through the system, while the second destroys the coherence via a dephasing mechanism. By studying the unraveling of stochastic quantum trajectories associated with the continuous monitoring protocols, we present a transition for the scaling of the averaged trajectory entanglement entropies, from critical scaling to area-law behavior. Our work provides an alternative perspective on the measurement-induced phase transition: the measurement can be viewed as monitoring and registering quantum jumps, offering an intriguing extension of these phase transitions through the long-established realm of quantum optics.

Distributed geometric quantum computation based on the optimized-control-technique in a cavity-atom system via exchanging virtual photons

We propose a scheme for quantum geometric computation on a fiber-cavity-fiber system, in which two atoms are located in two single-mode cavities, respectively, connected with each other by optical fiber. This scheme not only has the feature of virtual excitation of photons in the cavity quantum electrodynamics (CQED) that can reduce the effect of decay effectively but also has the advantage of geometric phase to withstand noises due to its built-in noise-resilience feature and robust merit. Specifically, our proposal combined with optimized-control-technology (OCT) can reduce gate operation error by adjusting the time-dependent amplitude and phase of the resonant field which further enhances the robustness of the quantum operation. The robustness against decoherence is demonstrated numerically and the scheme may be applied in the remote quantum information processing tasks and quantum computation.

Effects of dissipation induced blockade on the dynamics of two qubits without direct interaction

We study the effects of dissipation induced blockade on the dynamics of an open quantum system having two qubits in nonequilibrium independent baths. The qubits are driven by a classical field with a temporally modulated detuning. The introduction of blockade induced via two effective baths together with the effect of the driving field enable us to observe maximal entanglement oscillation of about unity that decays with a quasi-steady entanglement state oscillating about the 1/2 limit with adjustable decay rate. When the temperature difference between two baths is not large, maximal entanglement oscillation can still be observed in the model. In addition, the adjustment of the nonequilibrium thermal baths by modulating the dissipation and the application of time-dependent detuning give rise to rich entanglement dynamics. We further demonstrate numerically the practical implementation of the proposed scheme with a universal cavity QED setting.

One-step implementation of Toffoli gate for neutral atoms based on unconventional Rydberg pumping

Compared with the idea of universal quantum computation, a direct synthesis of a multiqubit logic gate can greatly improve the efficiency of quantum information processing tasks. Here we propose an efficient scheme to implement a three-qubit controlled-not (Toffoli) gate of neutral atoms based on unconventional Rydberg pumping. By adjusting the strengths of Rabi frequencies of driving fields, the Toffoli gate can be achieved within one step, which is also insensitive to the fluctuation of the Rydberg-Rydberg interaction. Considering different atom alignments, we can obtain a high-fidelity Toffoli gate at the same operation time ∼7 μs. In addition, our scheme can be further extended to the four-qubit case without altering the operating time.

Discrimination of enantiomers through quantum interference and quantum Zeno effect

Quantum optical methods have great potential for highly efficient discrimination of chiral molecules. We propose quantum interference-based schemes of enantio-discrimination under microwave regime among molecular rotational states. The quantum interference between field-driven one- and two-photon transitions of two higher states is designed to be constructive for one enantiomer but destructive for the other, since a certain transition dipole moment can be set to change sign with enantiomers. Therefore, two enantiomers can evolve into entirely different states from the same ground state. Through strengthening the constructive interference, the quantum Zeno effect is found in one enantiomer and then its excitation is suppressed, which also enables the enantio-discrimination. We simulate the schemes for differentiating between S and R enantiomers of 1, 2-propanediol (C₃H₈O₂) molecules. With the analysis of the phase sensitivity to microwave fields and the effect of energy relaxations, the highly efficient enantio-discrimination of the 1, 2-propanediol molecules may be achieved.

One-way quantum state transfer in a lossy coupled-cavity array

Quantum state transfer plays an important role in quantum information processing, and it has been obtained many of the theoretical and experimental triumphs. But designing a dissipation-assisted scheme to transfer a quantum state is still by no means trivial. Here we put forward an easier scheme to dissipatively transfer an arbitrary quantum state from a sender to a receiver with two four-level atoms and three lasers in a lossy coupled-cavity array, and make the quantum state stable at the receiver via the photon loss of optical cavities. Owing to the assistance of the dissipation, the target state becomes the steady state of the whole process. Thus there is no requirement on external time-dependent controls. Furthermore, the atomic spontaneous emission can be significantly suppressed as the adiabatic elimination of the excited states. We also discuss the experimental feasibility of this scheme with the current experimental technologies and a high fidelity of the transferred state in the receiver can be above 98%.

Photon Pair Condensation by Engineered Dissipation

Dissipation can usually induce detrimental decoherence in a quantum system. However, engineered dissipation can be used to prepare and stabilize coherent quantum many-body states. Here, we show that, by engineering dissipators containing photon pair operators, one can stabilize an exotic dark state, which is a condensate of photon pairs with a phase-nematic order. In this system, the usual superfluid order parameter, i.e., single-photon correlation, is absent, while the photon pair correlation exhibits long-range order. Although the dark state is not unique due to multiple parity sectors, we devise an additional type of dissipators to stabilize the dark state in a particular parity sector via a diffusive annihilation process which obeys Glauber dynamics in an Ising model. Furthermore, we propose an implementation of these photon pair dissipators in circuit-QED architecture.

Photon-mediated interactions between quantum emitters in a diamond nanocavity

Photon-mediated interactions between quantum systems are essential for realizing quantum networks and scalable quantum information processing. We demonstrate such interactions between pairs of silicon-vacancy (SiV) color centers coupled to a diamond nanophotonic cavity. When the optical transitions of the two color centers are tuned into resonance, the coupling to the common cavity mode results in a coherent interaction between them, leading to spectrally resolved superradiant and subradiant states. We use the electronic spin degrees of freedom of the SiV centers to control these optically mediated interactions. Such controlled interactions will be crucial in developing cavity-mediated quantum gates between spin qubits and for realizing scalable quantum network nodes.

Dissipation-induced W state in a Rydberg-atom-cavity system

A dissipative scheme is proposed to prepare tripartite W state in a Rydberg-atom-cavity system. It is an organic combination of quantum Zeno dynamics, Rydberg antiblockade, and atomic spontaneous emission to turn the tripartite W state into the unique steady state of the whole system. The robustness against the loss of cavity and the feasibility of the scheme are demonstrated thoroughly by the current experimental parameters, which lead to a high fidelity above 98%.

Implementation of a Toffoli gate using an array of coupled cavities in a single step

The Toffoli gate (controlled-controlled-NOT gate) is one typical three-qubit gate, it plus a Hadamard gate form a universal set of gates in quantum computation. We present an efficient method to implement the Toffoli gate using an array of coupled cavities with one three-level atom in each cavity. The large detuning between atoms and classical (quantum) fields plays an important role and the gate is implemented in one-step. The quantum information is encoded into the low-lying states of identical atoms and it is convenient to address qubit individually. Based on the Markovian master equation, it is shown that the scheme to implement the Toffoli gate is robust against the decoherence.

Exponentially Enhanced Light-Matter Interaction, Cooperativities, and Steady-State Entanglement Using Parametric Amplification

We propose an experimentally feasible method for enhancing the atom-field coupling as well as the ratio between this coupling and dissipation (i.e., cooperativity) in an optical cavity. It exploits optical parametric amplification to exponentially enhance the atom-cavity interaction and, hence, the cooperativity of the system, with the squeezing-induced noise being completely eliminated. Consequently, the atom-cavity system can be driven from the weak-coupling regime to the strong-coupling regime for modest squeezing parameters, and even can achieve an effective cooperativity much larger than 100. Based on this, we further demonstrate the generation of steady-state nearly maximal quantum entanglement. The resulting entanglement infidelity (which quantifies the deviation of the actual state from a maximally entangled state) is exponentially smaller than the lower bound on the infidelities obtained in other dissipative entanglement preparations without applying squeezing. In principle, we can make an arbitrarily small infidelity. Our generic method for enhancing atom-cavity interaction and cooperativities can be implemented in a wide range of physical systems, and it can provide diverse applications for quantum information processing.

Engineering steady Knill-Laflamme-Milburn state of Rydberg atoms by dissipation

The Knill-Laflamme-Milburn (KLM) states have been proved to be a useful resource for quantum information processing [Nature409, 46 (2001)]. For atomic KLM states, several schemes have been put forward based on the time-dependent unitary dynamics, but the dissipative generation of these states has not been reported. This work discusses the possibility for creating different forms of bipartite KLM states in neutral atom system, where the spontaneous emission of excited Rydberg states, combined with the Rydberg antiblockade mechanism, is actively exploited to engineer a steady KLM state from an arbitrary initial state. The numerical simulation of the master equation signifies that a fidelity above 99% is available with the current experimental parameters.

Generation of steady entanglement via unilateral qubit driving in bad cavities

We propose a scheme for generating an entangled state for two atoms trapped in two separate cavities coupled to each other. The scheme is based on the competition between the unitary dynamics induced by the classical fields and the collective decays induced by the dissipation of two non-local bosonic modes. In this scheme, only one qubit is driven by external classical fields, whereas the other need not be manipulated via classical driving. This is meaningful for experimental implementation between separate nodes of a quantum network. The steady entanglement can be obtained regardless of the initial state, and the robustness of the scheme against parameter fluctuations is numerically demonstrated. We also give an analytical derivation of the stationary fidelity to enable a discussion of the validity of this regime. Furthermore, based on the dissipative entanglement preparation scheme, we construct a quantum state transfer setup with multiple nodes as a practical application.

Dissipative quantum error correction and application to quantum sensing with trapped ions

Quantum-enhanced measurements hold the promise to improve high-precision sensing ranging from the definition of time standards to the determination of fundamental constants of nature. However, quantum sensors lose their sensitivity in the presence of noise. To protect them, the use of quantum error-correcting codes has been proposed. Trapped ions are an excellent technological platform for both quantum sensing and quantum error correction. Here we present a quantum error correction scheme that harnesses dissipation to stabilize a trapped-ion qubit. In our approach, always-on couplings to an engineered environment protect the qubit against spin-flips or phase-flips. Our dissipative error correction scheme operates in a continuous manner without the need to perform measurements or feedback operations. We show that the resulting enhanced coherence time translates into a significantly enhanced precision for quantum measurements. Our work constitutes a stepping stone towards the paradigm of self-correcting quantum information processing.

Lyapunov-Based Feedback Preparation of GHZ Entanglement of $N$ -Qubit Systems

The Greenberger-Horne-Zeilinger (GHZ) entangled states are a typical class of entangled states in multiparticle systems and play an important role in the applications of quantum communication and quantum computation. For a general quantum system of qubits, degenerate measurement operators are often met, which cause the convergence obstacle in the state preparation or stabilization problem. This paper first generalizes the traditional quantum state continuous reduction theory to the case of a degenerate measurement operator and chooses a measurement operator for an arbitrarily given target GHZ entangled state, then presents a state stabilization control strategy based on the Lyapunov method and achieves the feedback preparation of the target GHZ state. In our stabilization strategy, we separate the target GHZ state and all the other GHZ states that often form the equilibrium points of the closed-loop system by dividing the state space into several different regions; and formally design a switching control law between the regions, which contains the control Hamiltonians to be constructed. By analyzing the stability of the closed-loop system in the different regions, we propose a systematic method for constructing the control Hamiltonians and solve the convergence problem caused by the degenerate measurement operator. The global stability of the whole closed-loop stochastic system is strictly proved. Also, we perform some simulation experiments on a three-qubit system and prepare a three-qubit GHZ entangled state. At the same time, the simulation results show the effectiveness of the switching control law and the construction method for the control Hamiltonians proposed in this paper.

Engineering steady-state entanglement via dissipation and quantum Zeno dynamics in an optical cavity

A new mechanism is proposed for dissipatively preparing maximal Bell entangled state of two atoms in an optical cavity. This scheme integrates the spontaneous emission, the light shift of atoms in the presence of dispersive microwave field, and the quantum Zeno dynamics induced by continuous coupling, to obtain a unique steady state irrespective of initial state. Even for a large cavity decay, a high-fidelity entangled state is achievable at a short convergence time, since the occupation of the cavity mode is inhibited by the Zeno requirement. Therefore, a low single-atom cooperativity C=g²/(κγ) is good enough for realizing a high fidelity of entanglement in a wide range of decoherence parameters. As a straightforward extension, the feasibility for preparation of two-atom Knill-Laflamme-Milburn state with the same mechanism is also discussed.

Dissipation-assisted spin squeezing of nitrogen-vacancy centers coupled to a rectangular hollow metallic waveguide

Spin squeezing has received much attention due to the interesting physics and important applications such as quantum metrology and quantum information processing. We here present a scheme to engineer stable spin squeezing in an array of nitrogen vacancy centers (NVCs) coupled to a rectangular hollow metallic waveguide. The remarkable feature of the waveguide as the common environment media is that one can switch on/off either the waveguide induced dipole-dipole interactions or correlated spontaneous emissions among the NVCs by designing their spatial separation. It permits us to achieve a dissipative Dicke model after the dipole-dipole interactions vanish due to destructive interference. With the external driving lasers on each NVC, a second-order phase transition is triggered, separating the steady state into two phases with and without collective spin squeezing. Supplying a physical realization of the dissipative Dicke model, our study gives a bridge between the generation of the stable spin squeezing and the phase transition physics.

Dissipative preparation of distributed steady entanglement: an approach of unilateral qubit driving

We propose a nonlocal scheme for preparing a distributed steady-state entanglement of two atoms trapped in separate optical cavities coupled through an optical fiber based on the combined effect of the unitary dynamics and dissipative process. In this scheme, only the qubit of one node is driven by an external classical field, while the other one does not need to be manipulated by an external field. This is meaningful for long distance quantum information processing tasks, and the experimental implementation is greatly simplified due to the unilateral manipulation on one node and the process of entanglement distribution can be avoided. This guarantees the absolute security of long distance quantum information processing tasks and makes the scheme more robust than that based on the unitary dynamics. We introduce the purity to characterize the mixture degree of the target steady-state. The steady entanglement can be obtained independent of the initial state. Furthermore, based on the dissipative entanglement preparation scheme, we construct a quantum teleportation setup with multiple nodes as a practical application, and the numerical simulation demonstrates the scheme can be realized effectively under the current experimental conditions..

Error-detected generation and complete analysis of hyperentangled Bell states for photons assisted by quantum-dot spins in double-sided optical microcavities

We construct an error-detected block, assisted by the quantum-dot spins in double-sided optical microcavities. With this block, we propose three error-detected schemes for the deterministic generation, the complete analysis, and the complete nondestructive analysis of hyperentangled Bell states in both the polarization and spatial-mode degrees of freedom of two-photon systems. In these schemes, the errors can be detected, which can improve their fidelities largely, far different from other previous schemes assisted by the interaction between the photon and the QD-cavity system. Our scheme for the deterministic generation of hyperentangled two-photon systems can be performed by repeat until success. These features make our schemes more useful in high-capacity quantum communication with hyperentanglement in the future.

Controllable and fast quantum-information transfer between distant nodes in two-dimensional networks

We construct shortcuts to adiabatic passage to achieve controllable and fast quantum-information transfer (QIT) between arbitrary two distant nodes in a two-dimensional (2D) quantum network. Through suitable designing of time-dependent Rabi frequencies, we show that perfect QIT between arbitrary two distant nodes can be rapidly achieved. Numerical simulations demonstrate that the proposal is robust to the decoherence caused by atomic spontaneous emission and cavity photon leakage. Additionally, the proposed scheme is also insensitive to the variations of the experimental parameters. Thus, the proposed scheme provides a new perspective on robust quantum information processing in 2D quantum networks.

Improving the stimulated Raman adiabatic passage via dissipative quantum dynamics

We propose a method to improve the stimulated Raman adiabatic passage (STIRAP) via dissipative quantum dynamics, taking into account the dephasing effects. Fast and robust population transfer can be obtained with the scheme by the designed pulses and detuning, even though the initial state of the system is imperfect. With a concrete three-level system as an example, the influences of the imperfect initial state, variations in the control parameters, and various dissipation effects are discussed in detail. The numerical simulation shows that the scheme is insensitive to moderate fluctuations of experimental parameters and the relatively large dissipation effects of the excited state. Furthermore, the dominant dissipative factors, namely, the dephasing effects of the ground states and the imperfect initial state are no longer undesirable, in fact, they are the important resources to the scheme. Therefore, the scheme could provide more choices for the realization of the complete population transfer in the strong dissipative fields where the standard stimulated Raman adiabatic passage or shortcut schemes are invalid.

Keldysh field theory for driven open quantum systems

Recent experimental developments in diverse areas-ranging from cold atomic gases to light-driven semiconductors to microcavity arrays-move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states and their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.

Scalable Dissipative Preparation of Many-Body Entanglement

We present a technique for the dissipative preparation of highly entangled multiparticle states of atoms coupled to common oscillator modes. By combining local spontaneous emission with coherent couplings, we engineer many-body dissipation that drives the system from an arbitrary initial state into a Greenberger-Horne-Zeilinger state. We demonstrate that using our technique highly entangled steady states can be prepared efficiently in a time that scales polynomially with the system size. Our protocol assumes generic couplings and will thus enable the dissipative production of multiparticle entanglement in a wide range of physical systems. As an example, we demonstrate the feasibility of our scheme in state-of-the-art trapped-ion systems.

Dissipative Quantum Control of a Spin Chain

A protocol is discussed for preparing a spin chain in a generic many-body state in the asymptotic limit of tailored nonunitary dynamics. The dynamics require the spectral resolution of the target state, optimized coherent pulses, engineered dissipation, and feedback. As an example, we discuss the preparation of an entangled antiferromagnetic state, and argue that the procedure can be applied to chains of trapped ions or Rydberg atoms.

Transient and steady-state entanglement mediated by three-dimensional plasmonic waveguides

Entanglement between two qubits (two level atoms) mediated by surface plasmons in three-dimensional plasmonic waveguides is studied using a quantum master equation formalism. Two types of waveguides, a nanowire and a V-shaped channel cut in a flat metal plane, are considered. The Green functions for the waveguides, which rigorously describes the dissipative qubit environment, are calculated numerically using a direct finite-difference time-domain (FDTD) solution of Maxwell's equations. Finite-length effects are shown to play a crucial role in enhancing entanglement, and resonant-length plasmonic waveguides can provide higher entanglement between qubits than infinite-length waveguides. It is also shown that coupling slots can improve entanglement via stronger qubit-waveguide coupling, for both the infinite- and finite-waveguide cases. The formalism used in the paper can be applied to a wide range of plasmonic waveguides.

Implementation of quantum state manipulation in a dissipative cavity

We discuss a method to perform dissipation-assisted quantum state manipulation in a cavity. We show that atomic spontaneous emission and cavity decay might be exploited to drive many atoms into many-body steady-state entanglement. Our protocol offers a dramatic improvement in fidelity when noise strength increases. Moreover, the dephasing noise is suppressed effectively by showing that high-fidelity target state can be obtained in a dissipative environment.

Heralded quantum gates with integrated error detection in optical cavities

We propose and analyze heralded quantum gates between qubits in optical cavities. They employ an auxiliary qubit to report if a successful gate occurred. In this manner, the errors, which would have corrupted a deterministic gate, are converted into a nonunity probability of success: once successful, the gate has a much higher fidelity than a similar deterministic gate. Specifically, we describe that a heralded, near-deterministic controlled phase gate (CZ gate) with the conditional error arbitrarily close to zero and the success probability that approaches unity as the cooperativity of the system, C, becomes large. Furthermore, we describe an extension to near-deterministic N-qubit Toffoli gate with a favorable error scaling. These gates can be directly employed in quantum repeater networks to facilitate near-ideal entanglement swapping, thus greatly speeding up the entanglement distribution.

Cavity-modified collective Rayleigh scattering of two atoms

We report on the observation of cooperative radiation of exactly two neutral atoms strongly coupled to the single mode field of an optical cavity, which is close to the lossless-cavity limit. Monitoring the cavity output power, we observe constructive and destructive interference of collective Rayleigh scattering for certain relative distances between the two atoms. Because of cavity backaction onto the atoms, the cavity output power for the constructive two-atom case (N=2) is almost equal to the single-emitter case (N=1), which is in contrast to free-space where one would expect an N^{2} scaling of the power. These effects are quantitatively explained by a classical model as well as by a quantum mechanical model based on Dicke states. We extract information on the relative phases of the light fields at the atom positions and employ advanced cooling to reduce the jump rate between the constructive and destructive atom configurations. Thereby we improve the control over the system to a level where the implementation of two-atom entanglement schemes involving optical cavities becomes realistic.

Preparation of three-dimensional entanglement for distant atoms in coupled cavities via atomic spontaneous emission and cavity decay

We propose a dissipative scheme to prepare a three-dimensional entangled state for two atoms trapped in separate coupled cavities. Our work shows that both atomic spontaneous emission and cavity decay, which are two typical obstacles in unitary-dynamics-based schemes, are no longer detrimental, but necessary for three-dimensional entangled state preparation without specifying initial state and controlling the evolution time precisely. Final numerical simulation with one group of experimental parameters indicates that the performance of our scheme could be better than the unitary-dynamics-based scheme.

Coherent quantum dynamics in steady-state manifolds of strongly dissipative systems

Recently, it has been realized that dissipative processes can be harnessed and exploited to the end of coherent quantum control and information processing. In this spirit, we consider strongly dissipative quantum systems admitting a nontrivial manifold of steady states. We show how one can enact adiabatic coherent unitary manipulations, e.g., quantum logical gates, inside this steady-state manifold by adding a weak, time-rescaled, Hamiltonian term into the system's Liouvillian. The effective long-time dynamics is governed by a projected Hamiltonian which results from the interplay between the weak unitary control and the fast relaxation process. The leakage outside the steady-state manifold entailed by the Hamiltonian term is suppressed by an environment-induced symmetrization of the dynamics. We present applications to quantum-computation in decoherence-free subspaces and noiseless subsystems and numerical analysis of nonadiabatic errors.

Preparation of two-qubit steady entanglement through driving a single qubit

Inspired by a recent paper [J. Phys. B 47, 055502 (2014)], we propose a simplified scheme to generate and stabilize a Bell state of two qubits coupled to a resonator. In the scheme only one qubit is needed to be driven by external classical fields, and the entanglement dynamics is independent of the phases of these fields and insensitive to their amplitude fluctuations. This is a distinct advantage as compared with the previous ones that require each qubit to be addressed by well-controlled classical fields. Numerical simulation shows that the steady singlet state with high fidelity can be obtained with currently available techniques in circuit quantum electrodynamics.

Analytic solution for heat flow through a general harmonic network

We present an analytic expression for the heat current through a general harmonic network coupled with Ohmic reservoirs. We use a method that enables us to express the stationary state of the network in terms of the eigenvectors and eigenvalues of a generalized cubic eigenvalue problem. In this way, we obtain exact formulas for the heat current and the local temperature inside the network. Our method does not rely on the usual assumptions of weak coupling to the environments or on the existence of an infinite cutoff in the environmental spectral densities. We use this method to study nonequilibrium processes without the weak coupling and Markovian approximations. As a first application of our method, we revisit the problem of heat conduction in two- and three-dimensional crystals with binary mass disorder. We complement previous results showing that for small systems the scaling of the heat current with the system size greatly depends on the strength of the interaction between system and reservoirs. This somewhat counterintuitive result seems not to have been noticed before.

Incoherent control of the retinal isomerization in rhodopsin

We propose to control the retinal photoisomerization yield through the backaction dynamics imparted by a nonselective optical measurement of the molecular electronic state. This incoherent effect is easier to implement than comparable coherent pulse shaping techniques, and is also robust to environmental noise. A numerical simulation of the quantum dynamics shows that the isomerization yield of this important biomolecule can be substantially increased above the natural limit.

Quantum information-geometry of dissipative quantum phase transitions

A general framework for analyzing the recently discovered phase transitions in the steady state of dissipation-driven open quantum systems is still lacking. To fill this gap, we extend the so-called fidelity approach to quantum phase transitions to open systems whose steady state is a Gaussian fermionic state. We endow the manifold of correlation matrices of steady states with a metric tensor g measuring the distinguishability distance between solutions corresponding to a different set of control parameters. The phase diagram can then be mapped out in terms of the scaling behavior of g and connections with the Liouvillean gap and the model correlation functions unveiled. We argue that the fidelity approach, thanks to its differential-geometric and information-theoretic nature, provides insights into dissipative quantum critical phenomena as well as a general and powerful strategy to explore them.

Autonomously stabilized entanglement between two superconducting quantum bits

Quantum error correction codes are designed to protect an arbitrary state of a multi-qubit register from decoherence-induced errors, but their implementation is an outstanding challenge in the development of large-scale quantum computers. The first step is to stabilize a non-equilibrium state of a simple quantum system, such as a quantum bit (qubit) or a cavity mode, in the presence of decoherence. This has recently been accomplished using measurement-based feedback schemes. The next step is to prepare and stabilize a state of a composite system. Here we demonstrate the stabilization of an entangled Bell state of a quantum register of two superconducting qubits for an arbitrary time. Our result is achieved using an autonomous feedback scheme that combines continuous drives along with a specifically engineered coupling between the two-qubit register and a dissipative reservoir. Similar autonomous feedback techniques have been used for qubit reset, single-qubit state stabilization, and the creation and stabilization of states of multipartite quantum systems. Unlike conventional, measurement-based schemes, the autonomous approach uses engineered dissipation to counteract decoherence, obviating the need for a complicated external feedback loop to correct errors. Instead, the feedback loop is built into the Hamiltonian such that the steady state of the system in the presence of drives and dissipation is a Bell state, an essential building block for quantum information processing. Such autonomous schemes, which are broadly applicable to a variety of physical systems, as demonstrated by the accompanying paper on trapped ion qubits, will be an essential tool for the implementation of quantum error correction.

Heralded entanglement of two ions in an optical cavity

We demonstrate precise control of the coupling of each of two trapped ions to the mode of an optical resonator. When both ions are coupled with near-maximum strength, we generate ion-ion entanglement heralded by the detection of two orthogonally polarized cavity photons. The entanglement fidelity with respect to the Bell state Ψ+ reaches F≥(91.9±2.5)%. This result represents an important step toward distributed quantum computing with cavities linking remote atom-based registers.

Quantum teleportation of dynamics and effective interactions between remote systems

Most protocols for quantum information processing consist of a series of quantum gates, which are applied sequentially. In contrast, interactions between matter and fields, for example, as well as measurements such as homodyne detection of light are typically continuous in time. We show how the ability to perform quantum operations continuously and deterministically can be leveraged for inducing nonlocal dynamics between two separate parties. We introduce a scheme for the engineering of an interaction between two remote systems and present a protocol that induces a dynamics in one of the parties that is controlled by the other one. Both schemes apply to continuous variable systems, run continuously in time, and are based on real-time feedback.

Ground-state cooling of a single atom at the center of an optical cavity

A single neutral atom is trapped in a three-dimensional optical lattice at the center of a high-finesse optical resonator. Using fluorescence imaging and a shiftable standing-wave trap, the atom is deterministically loaded into the maximum of the intracavity field where the atom-cavity coupling is strong. After 5 ms of Raman sideband cooling, the three-dimensional motional ground state is populated with a probability of (89±2)%. Our system is the first to simultaneously achieve quantum control over all degrees of freedom of a single atom: its position and momentum, its internal state, and its coupling to light.

Dissipative preparation of spin squeezed atomic ensembles in a steady state

We present and analyze a new approach for the generation of atomic spin-squeezed states. Our method involves the collective coupling of an atomic ensemble to a decaying mode of an open optical cavity. We demonstrate the existence of a collective atomic dark state, decoupled from the radiation field. By explicitly constructing this state we find that it can feature spin squeezing bounded only by the Heisenberg limit. We show that such dark states can be deterministically prepared via dissipative means, thus turning dissipation into a resource for entanglement. The scaling of the phase sensitivity taking realistic imperfections into account is discussed.

Dissipation-assisted quantum information processing with trapped ions

We introduce a scheme to perform dissipation-assisted quantum information processing in ion traps considering realistic decoherence rates, for example, due to motional heating. By means of continuous sympathetic cooling, we overcome the trap heating by showing that the damped vibrational excitations can still be exploited to mediate coherent interactions as well as collective dissipative effects. We describe how to control their relative strength experimentally, allowing for protocols of coherent or dissipative generation of entanglement. This scheme can be scaled to larger ion registers for coherent or dissipative many-body quantum simulations.

Precisely timing dissipative quantum information processing

Dissipative engineering constitutes a framework within which quantum information processing protocols are powered by system-environment interaction rather than by unitary dynamics alone. This framework embraces noise as a resource and, consequently, offers a number of advantages compared to one based on unitary dynamics alone, e.g., that the protocols are typically independent of the initial state of the system. However, the time independent nature of this scheme makes it difficult to imagine precisely timed sequential operations, conditional measurements, or error correction. In this work, we provide a path around these challenges, by introducing basic dissipative gadgets which allow us to precisely initiate, trigger, and time dissipative operations while keeping the system Liouvillian time independent. These gadgets open up novel perspectives for thinking of timed dissipative quantum information processing. As an example, we sketch how measurement-based computation can be simulated in the dissipative setting.