Enhancing detection of topological order by local error correction

The exploration of topologically-ordered states of matter is a long-standing goal at the interface of several subfields of the physical sciences. Such states feature intriguing physical properties such as long-range entanglement, emergent gauge fields and non-local correlations, and can aid in realization of scalable fault-tolerant quantum computation. However, these same features also make creation, detection, and characterization of topologically-ordered states particularly challenging. Motivated by recent experimental demonstrations, we introduce a paradigm for quantifying topological states-locally error-corrected decoration (LED)-by combining methods of error correction with ideas of renormalization-group flow. Our approach allows for efficient and robust identification of topological order, and is applicable in the presence of incoherent noise sources, making it particularly suitable for realistic experiments. We demonstrate the power of LED using numerical simulations of the toric code under a variety of perturbations. We subsequently apply it to an experimental realization, providing new insights into a quantum spin liquid created on a Rydberg-atom simulator. Finally, we extend LED to generic topological phases, including those with non-abelian order.

Phonon Laser in the Quantum Regime

We demonstrate a trapped-ion system with two competing dissipation channels, implemented independently on two ion species cotrapped in a Paul trap. By controlling coherent spin-oscillator couplings and optical pumping rates we explore the phase diagram of this system, which exhibits a regime analogous to that of a (phonon) laser but operates close to the quantum ground state with an average phonon number of n[over ¯]<10. We demonstrate phase locking of the oscillator to an additional resonant drive, and also observe the phase diffusion of the resulting state under dissipation by reconstructing the quantum state from a measurement of the characteristic function.

Chemical reactivity under collective vibrational strong coupling

Recent experiments of chemical reactions in optical cavities have shown great promise to alter and steer chemical reactions, but still remain poorly understood theoretically. In particular, the origin of resonant effects between the cavity and certain vibrational modes in the collective limit is still subject to active research. In this paper, we study the unimolecular dissociation reactions of many molecules, collectively interacting with an infrared cavity mode, through their vibrational dipole moment. We find that the reaction rate can slow down by increasing the number of aligned molecules, if the cavity mode is resonant with a vibrational mode of the molecules. We also discover a simple scaling relation that scales with the collective Rabi splitting, to estimate the onset of reaction rate modification by collective vibrational strong coupling and numerically demonstrate these effects for up to 104 molecules.

Cavity-Modified Unimolecular Dissociation Reactions via Intramolecular Vibrational Energy Redistribution

While the emerging field of vibrational polariton chemistry has the potential to overcome traditional limitations of synthetic chemistry, the underlying mechanism is not yet well understood. Here, we explore how the dynamics of unimolecular dissociation reactions that are rate-limited by intramolecular vibrational energy redistribution (IVR) can be modified inside an infrared optical cavity. We study a classical model of a bent triatomic molecule, where the two outer atoms are bound by anharmonic Morse potentials to the center atom coupled to a harmonic bending mode. We show that an optical cavity resonantly coupled to particular anharmonic vibrational modes can interfere with IVR and alter unimolecular dissociation reaction rates when the cavity mode acts as a reservoir for vibrational energy. These results lay the foundation for further theoretical work toward understanding the intriguing experimental results of vibrational polaritonic chemistry within the context of IVR.

Entangled photons from composite cascade emitters

One of the most versatile sources for entangled photons are emitters that interact via more than one tunable mechanism. Here, we demonstrate how hybridization and dipole-dipole interactions-potentially simultaneously available in colloidal quantum dots and molecular aggregates-leveraged in conjunction can couple simple, well understood emitters into composite emitters with flexible control over the level structure. We show that cascade decay through carefully designed level structures can result in emission of frequency-entangled photons with Bell states and three-photon GHZ states as example cases. These results pave the way toward rational design of quantum optical emitters of entangled photons.

Defect Polaritons from First Principles

Control over the optical properties of defects in solid-state materials is necessary for their application in quantum technologies. In this study, we demonstrate, from first principles, how to tune these properties via the formation of defect polaritons in an optical cavity. We show that the polaritonic splitting that shifts the absorption energy of the lower polariton is much higher than can be expected from a Jaynes-Cummings interaction. We also find that the absorption intensity of the lower polariton increases by several orders of magnitude, suggesting a possible route toward overcoming phonon-limited single-photon emission from defect centers. These findings are a result of an effective continuum of electronic transitions near the lowest-lying electronic transition that dramatically enhances the strength of the light-matter interaction. We expect our findings to spur experimental investigations of strong light-matter coupling between defect centers and cavity photons for applications in quantum technologies.

Controlling Interactions between Quantum Emitters Using Atom Arrays

We investigate the potential for two-dimensional atom arrays to modify the radiation and interaction of individual quantum emitters. Specifically, we demonstrate that control over the emission linewidths, resonant frequency shifts, and local driving field enhancement in impurity atoms is possible due to strong dipole-dipole interactions within ordered, subwavelength atom array configurations. We demonstrate that these effects can be used to dramatically enhance coherent dipole-dipole interactions between distant impurity atoms within an atom array. Possible experimental realizations and potential applications are discussed.

Cooperative Breakdown of the Oscillator Blockade in the Dicke Model

The Dicke model, which describes the coupling of an ensemble of spins to a harmonic oscillator, is known for its superradiant phase transition, which can both be observed in the ground state in a purely Hamiltonian setting, as well as in the steady state of an open-system Dicke model with dissipation. We demonstrate that, in addition, the dissipative Dicke model can undergo a second phase transition to a nonstationary phase, characterized by unlimited heating of the harmonic oscillator. Identifying the mechanism of the phase transition and deriving the scaling of the critical coupling with the system size we conclude that the novel phase transition can be understood as a cooperative breakdown of the oscillator blockade which otherwise prevents higher excitation of the system. We discuss an implementation with trapped ions and investigate the role of cooling, by which the breakdown can be suppressed.

Optical Control of a Single Nuclear Spin in the Solid State

We demonstrate a novel method for coherent optical manipulation of individual nuclear spins in the solid state, mediated by the electronic states of a proximal quantum emitter. Specifically, using the nitrogen-vacancy (NV) color center in diamond, we demonstrate control of a proximal ^{14}N nuclear spin via an all-optical Raman technique. We evaluate the extent to which the intrinsic physical properties of the NV center limit the performance of coherent control, and we find that it is ultimately constrained by the relative rates of transverse hyperfine coupling and radiative decay in the NV center's excited state. Possible extensions and applications to other color centers are discussed.

Topological Quantum Optics Using Atomlike Emitter Arrays Coupled to Photonic Crystals

We propose an experimentally feasible nanophotonic platform for exploring many-body physics in topological quantum optics. Our system is composed of a two-dimensional lattice of nonlinear quantum emitters with optical transitions embedded in a photonic crystal slab. The emitters interact through the guided modes of the photonic crystal, and a uniform magnetic field gives rise to large topological band gaps, robust edge states, and a nearly flat band with a nonzero Chern number. The presence of a topologically nontrivial nearly flat band paves the way for the realization of fractional quantum Hall states and fractional topological insulators in a topological quantum optical setting.

Quantum Nonlinear Optics in Atomically Thin Materials

We show that a nonlinear optical response associated with a resonant, atomically thin material can be dramatically enhanced by placing it in front of a partially reflecting mirror, rendering otherwise weakly nonlinear systems suitable for experiments and applications involving quantum nonlinear optics. Our approach exploits the nonlinear response of long-lived polariton resonances that arise at particular distances between the material and the mirror. The scheme is entirely based on free-space optics, eliminating the need for cavities or complex nanophotonic structures. We analyze a specific implementation based on exciton-polariton resonances in two-dimensional semiconductors and discuss the role of imperfections and loss.

Topological Quantum Optics in Two-Dimensional Atomic Arrays

We demonstrate that two-dimensional atomic emitter arrays with subwavelength spacing constitute topologically protected quantum optical systems where the photon propagation is robust against large imperfections while losses associated with free space emission are strongly suppressed. Breaking time-reversal symmetry with a magnetic field results in gapped photonic bands with nontrivial Chern numbers and topologically protected, long-lived edge states. Due to the inherent nonlinearity of constituent emitters, such systems provide a platform for exploring quantum optical analogs of interacting topological systems.

Cooperative Resonances in Light Scattering from Two-Dimensional Atomic Arrays

We consider light scattering off a two-dimensional (2D) dipolar array and show how it can be tailored by properly choosing the lattice constant of the order of the incident wavelength. In particular, we demonstrate that such arrays can operate as a nearly perfect mirror for a wide range of incident angles and frequencies, and shape the emission pattern from an individual quantum emitter into a well-defined, collimated beam. These results can be understood in terms of the cooperative resonances of the surface modes supported by the 2D array. Experimental realizations are discussed, using ultracold arrays of trapped atoms and excitons in 2D semiconductor materials, as well as potential applications ranging from atomically thin metasurfaces to single photon nonlinear optics and nanomechanics.

Certifying separability in symmetric mixed states of N qubits, and superradiance

Separability criteria are typically of the necessary, but not sufficient, variety, in that satisfying some separability criterion, such as positivity of eigenvalues under partial transpose, does not strictly imply separability. Certifying separability amounts to proving the existence of a decomposition of a target mixed state into some convex combination of separable states; determining the existence of such a decomposition is "hard." We show that it is effective to ask, instead, if the target mixed state "fits" some preconstructed separable form, in that one can generate a sufficient separability criterion relevant to all target states in some family by ensuring enough degrees of freedom in the preconstructed separable form. We demonstrate this technique by inducing a sufficient criterion for "diagonally symmetric" states of N qubits. A sufficient separability criterion opens the door to study precisely how entanglement is (not) formed; we use ours to prove that, counterintuitively, entanglement is not generated in idealized Dicke model superradiance despite its exemplification of many-body effects. We introduce a quantification of the extent to which a given preconstructed parametrization comprises the set of all separable states; for "diagonally symmetric" states our preconstruction is shown to be fully complete. This implies that our criterion is necessary in addition to sufficient, among other ramifications which we explore.

Quantum phases of quadrupolar Fermi gases in optical lattices

We introduce a new platform for quantum simulation of many-body systems based on nonspherical atoms or molecules with zero dipole moments but possessing a significant value of electric quadrupole moments. We consider a quadrupolar Fermi gas trapped in a 2D square optical lattice, and show that the peculiar symmetry and broad tunability of the quadrupole-quadrupole interaction results in a rich phase diagram encompassing unconventional BCS and charge density wave phases, and opens up a perspective to create a topological superfluid. Quadrupolar species, such as metastable alkaline-earth atoms and homonuclear molecules, are stable against chemical reactions and collapse and are readily available in experiment at high densities.

Ion crystal transducer for strong coupling between single ions and single photons

A new approach for the realization of a quantum interface between single photons and single ions in an ion crystal is proposed and analyzed. In our approach the coupling between a single photon and a single ion is enhanced via the collective degrees of freedom of the ion crystal. Applications including single-photon generation, a memory for a quantum repeater, and a deterministic photon-photon, photon-phonon, or photon-ion entangler are discussed.

All-optical Fresnel lens in coherent media: controlling image with image

We theoretically explore an all-optical method for generating tunable diffractive Fresnel lenses in coherent media based on electromagnetically induced transparency. In this method, intensity-modulated images in coupling light fields can pattern the coherent media to induce the desired modulo-2π quadratic phase profiles for the lenses to diffract probe light fields. We characterize the focusing and imaging properties of the induced lenses. In particular, we show that the images in coupling fields can flexibly control the images in probe fields by diffraction, where large focal length tunability from 1 m to infinity and high output (∼ 88% diffraction efficiency) can be achieved. Additionally, we also find that the induced Fresnel lenses can be rapidly modulated with megahertz refresh rates using image-bearing square pulse trains in coupling fields. Our proposed lenses may find a wide range of applications for multimode all-optical signal processing in both the classical and quantum regimes.

Two-dimensional all-optical spatial light modulation with high speed in coherent media

We show theoretical evidence that coherent systems based on electromagnetically induced transparency (EIT) can function as optically addressed spatial light modulators with megahertz modulation rates. The transverse spatial properties of cw probe fields can be modulated fast using two-dimensional optical patterns. To exemplify our proposal, we study real-time generation and manipulation of Laguerre-Gaussian beams by means of phase or amplitude modulation using flat-top image-bearing pulse trains as coupling fields in low-cost hot vapor EIT systems.

Tunable negative refraction without absorption via electromagnetically induced chirality

We show that negative refraction with minimal absorption can be obtained by means of quantum interference effects similar to electromagnetically induced transparency (EIT). Coupling a magnetic dipole transition coherently with an electric dipole transition leads to electromagnetically induced chirality, which can provide negative refraction without requiring negative permeability and also suppress absorption. This technique allows negative refraction in the optical regime at densities where the magnetic susceptibility is still small and with refraction/absorption ratios that are orders of magnitude larger than those achievable previously. Furthermore, the refractive index can be fine-tuned, which is essential for practical realization of subdiffraction-limit imaging. As with EIT, electromagnetically induced chirality should be applicable to a wide range of systems.

Entanglement of atomic ensembles by trapping correlated photon states

We describe a general technique that allows for an ideal transfer of quantum correlations between light fields and metastable states of matter. The technique is based on trapping quantum states of photons in coherently driven atomic media, in which the group velocity is adiabatically reduced to zero. We discuss possible applications such as quantum state memories, generation of squeezed atomic states, preparation of entangled atomic ensembles, quantum information processing, and quantum networking.