Vacuum Rabi splitting in a semiconductor circuit QED system

Nonadiabatic Field with Triangle Window Functions on Quantum Phase Space

Recent progress on the constraint coordinate-momentum phase space (CPS) formulation of finite-state quantum systems has revealed that the triangle window function approach is an isomorphic representation of the exact population-population correlation function of the two-state system. We use the triangle window (TW) function and the CPS mapping kernel element to formulate a novel useful representation of discrete electronic degrees of freedom (DOFs). When it is employed with nonadiabatic field (NaF) dynamics, a new variant of the NaF approach (i.e., NaF-TW) is proposed. The NaF-TW expression of the population of any adiabatic state is always positive semidefinite. Extensive benchmark tests of model systems in both the condensed phase and gas phase demonstrate that the NaF-TW approach is able to faithfully capture the dynamical interplay between electronic and nuclear DOFs in a broad region, including where the states remain coupled all the time, as well as where the bifurcation characteristic of nuclear motion is important.

Nonadiabatic Field on Quantum Phase Space: A Century after Ehrenfest

Nonadiabatic transition dynamics lies at the core of many electron/hole transfer, photoactivated, and vacuum field-coupled processes. About a century after Ehrenfest proposed "Phasenraum" and the Ehrenfest theorem, we report a conceptually novel trajectory-based nonadiabatic dynamics approach, nonadiabatic field (NAF), based on a generalized exact coordinate-momentum phase space formulation of quantum mechanics. It does not employ the conventional Born-Oppenheimer or Ehrenfest trajectory in the nonadiabatic coupling region. Instead, in NAF the equations of motion of the independent trajectory involve a nonadiabatic nuclear force term in addition to an adiabatic nuclear force term of a single electronic state. A few benchmark tests for gas phase and condensed phase systems indicate that NAF offers a practical tool to capture the correct correlation of electronic and nuclear dynamics for processes where the states remain coupled all the time as well as for the asymptotic region where the coupling of electronic states vanishes.

Quantum resources for energy storage

Recently the possibility to exploit quantum-mechanical effects to increase the performance of energy storage has raised a great interest. It consists of N two-level systems coupled to a single photonic mode in a cavity. We demonstrate the emergence of a quantum advantage in the charging power on this collective model (Dicke Quantum Battery) with respect to the one in which each two-level system is coupled to its own separate cavity mode (Rabi Quantum Battery). Moreover, we discuss the model of a Quantum Supercapacitor. This consists of two chains, one containing electrons and the other one holes, hosted by arrays of double quantum dots. The two chains are in close proximity and embedded in the same photonic cavity, in the same spirit of the Dicke model. We find the phase diagram of this model showing that, when transitioning from the ferro/antiferromagnetic to the superradiant phase, the quantum capacitance of the model is greatly enhanced.

Microwave-Cavity-Detected Spin Blockade in a Few-Electron Double Quantum Dot

We investigate spin states of few electrons in a double quantum dot by coupling them to a magnetic field resilient NbTiN microwave resonator. The electric field of the resonator couples to the electric dipole moment of the charge states in the double dot. For a two-electron state the spin-triplet state has a vanishing electric dipole moment and can therefore be distinguished from the spin-singlet state. This way the charge dipole sensitivity of the resonator response is converted to a spin selectivity. We thereby investigate Pauli spin blockade known from transport experiments at finite source-drain bias. In addition we find an unconventional spin-blockade triggered by the absorption of resonator photons.

Multielectron Ground State Electroluminescence

The ground state of a cavity-electron system in the ultrastrong coupling regime is characterized by the presence of virtual photons. If an electric current flows through this system, the modulation of the light-matter coupling induced by this nonequilibrium effect can induce an extracavity photon emission signal, even when electrons entering the cavity do not have enough energy to populate the excited states. We show that this ground state electroluminescence, previously identified in a single-qubit system [Phys. Rev. Lett. 116, 113601 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.113601] can arise in a many-electron system. The collective enhancement of the light-matter coupling makes this effect, described beyond the rotating wave approximation, robust in the thermodynamic limit, allowing its observation in a broad range of physical systems, from a semiconductor heterostructure with flatband dispersion to various implementations of the Dicke model.

Vacuum induced transparency in metamaterials

For the cavity-based electromagnetically induced transparent (EIT), as the coherent driving field is enhanced by the optical cavity, the weak probe field can propagate through the atomic ensemble without absorption even if the driving field is weak. The extreme case of vacuum in the cavity is called "vacuum-induced transparency" (VIT) to distinguish it from the cavity EIT. Here we construct a new kind of cavity made of Metamaterials, i.e. ε-negative (EN) and μ-negative (MN) slabs, and study the VIT phenomena of the atomic ensemble doped within it. When the impedances of the MN and EN slabs are matched to each other and the dissipation of the material is small, it behaves as a surface plasmon cavity with a huge Q factor. And the VIT phenomenon in this cavity appears. By adjusting the position of atoms, the coupling strength between the atom and the structure could be changed. Two kinds of extremes of VIT, the coherent population trapping (CPT) and the Autler-Townes splitting (ATS), can be achieved in this system easily. Our proposal could be used in the realization of ultra-strong coupling and integrated devices on quantum memory or optical switch.

Virtual photons in the ground state of a dissipative system

Much of the novel physics predicted to be observable in the ultrastrong light–matter coupling regime rests on the hybridisation between states with different numbers of excitations, leading to a population of virtual photons in the system’s ground state. In this article, exploiting an exact diagonalisation approach, we derive both analytical and numerical results for the population of virtual photons in presence of arbitrary losses. Specialising our results to the case of Lorentzian resonances we then show that the virtual photon population is only quantitatively affected by losses, even when those become the dominant energy scale. Our results demonstrate most of the ultrastrong-coupling phenomenology can be observed in loss-dominated systems which are not even in the standard strong coupling regime. We thus open the possibility to investigate ultrastrong-coupling physics to platforms that were previously considered unsuitable due to their large losses.

Phenomena linked with ultrastrong coupling rely on the presence of virtual photons in the system’s ground state. In this article, using exact diagonalization, De Liberato shows that the population of ground state virtual photons is only quantitatively affected by losses.

Cavity QED with hybrid nanocircuits: from atomic-like physics to condensed matter phenomena

Circuit QED techniques have been instrumental in manipulating and probing with exquisite sensitivity the quantum state of superconducting quantum bits coupled to microwave cavities. Recently, it has become possible to fabricate new devices in which the superconducting quantum bits are replaced by hybrid mesoscopic circuits combining nanoconductors and metallic reservoirs. This mesoscopic QED provides a new experimental playground to study the light-matter interaction in electronic circuits. Here, we present the experimental state of the art of mesoscopic QED and its theoretical description. A first class of experiments focuses on the artificial atom limit, where some quasiparticles are trapped in nanocircuit bound states. In this limit, the circuit QED techniques can be used to manipulate and probe electronic degrees of freedom such as confined charges, spins, or Andreev pairs. A second class of experiments uses cavity photons to reveal the dynamics of electron tunneling between a nanoconductor and fermionic reservoirs. For instance, the Kondo effect, the charge relaxation caused by grounded metallic contacts, and the photo-emission caused by voltage-biased reservoirs have been studied. The tunnel coupling between nanoconductors and fermionic reservoirs also enable one to obtain split Cooper pairs, or Majorana bound states. Cavity photons represent a qualitatively new tool to study these exotic condensed matter states.

Threshold Dynamics of a Semiconductor Single Atom Maser

We demonstrate a single atom maser consisting of a semiconductor double quantum dot (DQD) that is embedded in a high-quality-factor microwave cavity. A finite bias drives the DQD out of equilibrium, resulting in sequential single electron tunneling and masing. We develop a dynamic tuning protocol that allows us to controllably increase the time-averaged repumping rate of the DQD at a fixed level detuning, and quantitatively study the transition through the masing threshold. We further examine the crossover from incoherent to coherent emission by measuring the photon statistics across the masing transition. The observed threshold behavior is in agreement with an existing single atom maser theory when small corrections from lead emission are taken into account.

Coupling a single electron spin to a microwave resonator: controlling transverse and longitudinal couplings

Microwave-frequency superconducting resonators are ideally suited to perform dispersive qubit readout, to mediate two-qubit gates, and to shuttle states between distant quantum systems. A prerequisite for these applications is a strong qubit-resonator coupling. Strong coupling between an electron-spin qubit and a microwave resonator can be achieved by correlating spin- and orbital degrees of freedom. This correlation can be achieved through the Zeeman coupling of a single electron in a double quantum dot to a spatially inhomogeneous magnetic field generated by a nearby nanomagnet. In this paper, we consider such a device and estimate spin-resonator couplings of order ∼1 MHz with realistic parameters. Further, through realistic simulations, we show that precise placement of the double-dot relative to the nanomagnet allows to select between a purely longitudinal coupling (commuting with the bare spin Hamiltonian) and a purely transverse (spin non-conserving) coupling. Additionally, we suggest methods to mitigate dephasing and relaxation channels that are introduced in this coupling scheme. This analysis gives a clear route toward the realization of coherent state transfer between a microwave resonator and a single electron spin in a GaAs double quantum dot with a fidelity above 90%. Improved dynamical decoupling sequences, low-noise environments, and longer-lived microwave cavity modes may lead to substantially higher fidelities in the near future.

Ground State Electroluminescence

Electroluminescence, the emission of light in the presence of an electric current, provides information on the allowed electronic transitions of a given system. It is commonly used to investigate the physics of strongly coupled light-matter systems, whose eigenfrequencies are split by the strong coupling with the photonic field of a cavity. Here we show that, together with the usual electroluminescence, systems in the ultrastrong light-matter coupling regime emit a uniquely quantum radiation when a flow of current is driven through them. While standard electroluminescence relies on the population of excited states followed by spontaneous emission, the process we describe herein extracts bound photons from the dressed ground state and it has peculiar features that unequivocally distinguish it from usual electroluminescence.

Bistable Photon Emission from a Solid-State Single-Atom Laser

We predict a bistability in the photon emission from a solid-state single-atom laser comprising a microwave cavity coupled to a voltage-biased double quantum dot. To demonstrate that the single-atom laser is bistable, we evaluate the photon emission statistics and show that the distribution takes the shape of a tilted ellipse. The switching rates of the bistability can be extracted from the electrical current and the shot noise in the quantum dots. This provides a means to control the photon emission statistics by modulating the electronic transport in the quantum dots. Our prediction is robust against moderate electronic decoherence and dephasing and is important for current efforts to realize single-atom lasers with gate-defined quantum dots as the gain medium.

Injection Locking of a Semiconductor Double Quantum Dot Micromaser

Emission linewidth is an important figure of merit for masers and lasers. We recently demonstrated a semiconductor double quantum dot (DQD) micromaser where photons are generated through single electron tunneling events. Charge noise directly couples to the DQD energy levels, resulting in a maser linewidth that is more than 100 times larger than the Schawlow-Townes prediction. Here we demonstrate a linewidth narrowing of more than a factor 10 by locking the DQD emission to a coherent tone that is injected to the input port of the cavity. We measure the injection locking range as a function of cavity input power and show that it is in agreement with the Adler equation. The position and amplitude of distortion sidebands that appear outside of the injection locking range are quantitatively examined. Our results show that this unconventional maser, which is impacted by strong charge noise and electron-phonon coupling, is well described by standard laser models.

Coupling Two Distant Double Quantum Dots with a Microwave Resonator

We fabricated a hybrid device with two distant graphene double quantum dots (DQDs) and a microwave resonator. A nonlinear response is observed in the resonator reflection amplitude when the two DQDs are jointly tuned to the vicinity of the degeneracy points. This observation can be well fitted by the Tavis-Cummings (T-C) model which describes two two-level systems coupling with one photonic field. Furthermore, the correlation between the DC currents in the two DQDs is studied. A nonzero cross-current correlation is observed which has been theoretically predicted to be an important sign of nonlocal coupling between two distant systems. Our results explore T-C physics in electronic transport and also contribute to the study of nonlocal transport and future implementations of remote electronic entanglement.

Charge Number Dependence of the Dephasing Rates of a Graphene Double Quantum Dot in a Circuit QED Architecture

We use an on-chip superconducting resonator as a sensitive meter to probe the properties of graphene double quantum dots at microwave frequencies. Specifically, we investigate the charge dephasing rates in a circuit quantum electrodynamics architecture. The dephasing rates strongly depend on the number of charges in the dots, and the variation has a period of four charges, over an extended range of charge numbers. Although the exact mechanism of this fourfold periodicity in dephasing rates is an open problem, our observations hint at the fourfold degeneracy expected in graphene from its spin and valley degrees of freedom.

Microwave Emission from Hybridized States in a Semiconductor Charge Qubit

We explore the microwave radiation emitted from a biased double quantum dot due to the inelastic tunneling of single charges. Radiation is detected over a broad range of detuning configurations between the dot energy levels, with pronounced maxima occurring in resonance with a capacitively coupled transmission line resonator. The power emitted for forward and reverse resonant detuning is found to be in good agreement with a rate equation model, which considers the hybridization of the individual dot charge states.

Clean carbon nanotubes coupled to superconducting impedance-matching circuits

Coupling carbon nanotube devices to microwave circuits offers a significant increase in bandwidth (BW) and signal-to-noise ratio. These facilitate fast non-invasive readouts important for quantum information processing, shot noise and correlation measurements. However, creation of a device that unites a low-disorder nanotube with a low-loss microwave resonator has so far remained a challenge, due to fabrication incompatibility of one with the other. Employing a mechanical transfer method, we successfully couple a nanotube to a gigahertz superconducting matching circuit and thereby retain pristine transport characteristics such as the control over formation of, and coupling strengths between, the quantum dots. Resonance response to changes in conductance and susceptance further enables quantitative parameter extraction. The achieved near matching is a step forward promising high-BW noise correlation measurements on high impedance devices such as quantum dot circuits.

Thermoelectric energy harvesting with quantum dots

We review recent theoretical work on thermoelectric energy harvesting in multi-terminal quantum-dot setups. We first discuss several examples of nanoscale heat engines based on Coulomb-coupled conductors. In particular, we focus on quantum dots in the Coulomb-blockade regime, chaotic cavities and resonant tunneling through quantum dots and wells. We then turn toward quantum-dot heat engines that are driven by bosonic degrees of freedom such as phonons, magnons and microwave photons. These systems provide interesting connections to spin caloritronics and circuit quantum electrodynamics.

Photon emission from a cavity-coupled double quantum dot

We study a voltage biased InAs double quantum dot (DQD) that is coupled to a superconducting transmission line resonator. Inelastic tunneling in the DQD is mediated by electron phonon coupling and coupling to the cavity mode. We show that electronic transport through the DQD leads to photon emission from the cavity at a rate of 10 MHz. With a small cavity drive field, we observe a gain of up to 15 in the cavity transmission. Our results are analyzed in the context of existing theoretical models and suggest that it may be necessary to account for inelastic tunneling processes that proceed via simultaneous emission of a phonon and a photon.

Hybrid microwave-cavity heat engine

We propose and analyze the use of hybrid microwave cavities as quantum heat engines. A possible realization consists of two macroscopically separated quantum-dot conductors coupled capacitively to the fundamental mode of a microwave cavity. We demonstrate that an electrical current can be induced in one conductor through cavity-mediated processes by heating up the other conductor. The heat engine can reach Carnot efficiency with optimal conversion of heat to work. When the system delivers the maximum power, the efficiency can be a large fraction of the Carnot efficiency. The heat engine functions even with moderate electronic relaxation and dephasing in the quantum dots. We provide detailed estimates for the electrical current and output power using realistic parameters.

Electron transport through a quantum dot assisted by cavity photons

We investigate transient transport of electrons through a single quantum dot controlled by a plunger gate. The dot is embedded in a finite wire with length Lx assumed to lie along the x-direction with a parabolic confinement in the y-direction. The quantum wire, originally with hard-wall confinement at its ends, ±Lx/2, is weakly coupled at t = 0 to left and right leads acting as external electron reservoirs. The central system, the dot and the finite wire, is strongly coupled to a single cavity photon mode. A non-Markovian density-matrix formalism is employed to take into account the full electron-photon interaction in the transient regime. In the absence of a photon cavity, a resonant current peak can be found by tuning the plunger-gate voltage to lift a many-body state of the system into the source-drain bias window. In the presence of an x-polarized photon field, additional side peaks can be found due to photon-assisted transport. By appropriately tuning the plunger-gate voltage, the electrons in the left lead are allowed to undergo coherent inelastic scattering to a two-photon state above the bias window if initially one photon was present in the cavity. However, this photon-assisted feature is suppressed in the case of a y-polarized photon field due to the anisotropy of our system caused by its geometry.