Light-matter interfaces enable the generation of entangled states of light and matter which can be exploited to steer the quantum state of matter through measurement of light and feedback. Here we consider continuous-time, interferometric homodyne measurements of light on an array of light-matter interfaces followed by local feedback acting on each material system individually. While the systems are physically noninteracting, the feedback master equation we derive describes driven-dissipative, interacting many-body quantum dynamics, and comprises pairwise Hamiltonian interactions and collective jump operators. We characterize the general class of driven-dissipative many-body systems which can be engineered in this way, and derive necessary conditions on models supporting nontrivial quantum dynamics beyond what can be generated by local operations and classical communication. We provide specific examples of models which allow for the creation of stationary many-particle entanglement, and the emulation of dissipative Ising models. Since the interaction between the systems is mediated via feedback only, there is no intrinsic limit on the range or geometry of the interaction, making the scheme quite versatile.
Light-matter interfaces enable the generation of entangled states of light and matter which can be exploited to steer the quantum state of matter through measurement of light and feedback. Here we consider continuous-time, interferometric homodyne measurements of light on an array of light-matter interfaces followed by local feedback acting on each material system individually. While the systems are physically noninteracting, the feedback master equation we derive describes driven-dissipative, interacting many-body quantum dynamics, and comprises pairwise Hamiltonian interactions and collective jump operators. We characterize the general class of driven-dissipative many-body systems which can be engineered in this way, and derive necessary conditions on models supporting nontrivial quantum dynamics beyond what can be generated by local operations and classical communication. We provide specific examples of models which allow for the creation of stationary many-particle entanglement, and the emulation of dissipative Ising models. Since the interaction between the systems is mediated via feedback only, there is no intrinsic limit on the range or geometry of the interaction, making the scheme quite versatile.
Quantum optics and ultracold gases are established fields, but they almost do not overlap: the quantum nature of light is typically neglected in works on ultracold atoms. In our work the quantumness of both light and ultracold matter plays a key role. First, we show that light is a quantum nondemolition (QND) probe of many-body phases: they can be distinguished by correlations and full distribution functions (we consider bosons, fermions, and dipolar molecules). Light is not only sensitive to densities, but also to the matter-field interference. Second, we prove that the measurement backaction constitutes a novel source of competitions in many-body systems, especially, for non-QND cases. This leads to a plethora of new phenomena: oscillations of multipartite entangled modes, protection and break-up of fermion pairs, antiferromagnetic orders, long-range pair tunnelling and entanglement beyond Hubbard models. We prove that feedback control induces phase transitions and tunes their universality class. Third, the quantization of trapping potential (quantum optical lattices) leads to novel phases, including both density orders (supersolids, density waves) and bond orders of matter fields (superfluid and supersolid dimers, trimers). Results beyond ultracold atoms include: We extend the paradigm of feedback control from the state control to control of phase transitions. We present the measurement backaction as a novel source of competitions in many-body physics. We merge quantum Zeno dynamics and non-Hermitian physics and show a novel type of Zeno phenomena with Raman transitions beyond Zeno dynamics. We propose quantum simulators based on collective light-matter interaction. Our models can be applied to arrays of other systems (qubits). In general, quantum measurements and feedback produce new phenomena untypical to both closed unitary systems and open dissipative ones in many-body physics.
Non-equilibrium quantum dynamics represents an emerging paradigm for condensed matter physics, quantum information science, and statistical mechanics. Strongly interacting Rydberg atoms offer an attractive platform to examine driven-dissipative dynamics of quantum spin models with long-range order. Here, we explore the conditions under which stationary many-body entanglement persists with near-unit fidelity and high scalability. In our approach, coherent many-body dynamics is driven by Rydberg-mediated laser transitions, while atoms at the lattice boundary locally reduce the entropy of the many-body system. Surprisingly, the many-body entanglement is established by continuously evolving a locally dissipative Rydberg system towards the steady state, precisely as with optical pumping. We characterize the dynamics of multipartite entanglement in an one-dimensional lattice by way of quantum uncertainty relations, and demonstrate the long-range behavior of the stationary entanglement with finite-size scaling. Our work opens a route towards dissipative preparation of many-body entanglement with unprecedented scaling behavior.
We present and discuss a master equation blueprint for a generic class of quantum measurement-feedback-based models of friction. A desired velocity-dependent friction force is realized on average by random repeated applications of unsharp momentum measurements followed by immediate outcome-dependent momentum displacements. The master equations can describe arbitrarily strong measurement-feedback processes as well as the weak continuous limit resembling diffusion master equations of Caldeira-Leggett type. We show that the special case of linear friction can be equivalently represented by an average over random position measurements with squeezing and position displacements as feedback. In fact, the dissipative continuous spontaneous localization model of objective wave-function collapse realizes this representation for a single quantum particle. We reformulate a consistent many-particle generalization of this model and highlight the possibility of feedback-induced correlations between otherwise noninteracting particles.
We are interested in dynamics of quantum many-body systems under continuous observation, and its physical realizations involving cold atoms in lattices. In the present work we focus on continuous measurement of atomic currents in lattice models, including the Hubbard model. We describe a Cavity QED setup, where measurement of a homodyne current provides a faithful representation of the atomic current as a function of time. We employ the quantum optical description in terms of a diffusive stochastic Schr\"odinger equation to follow the time evolution of the atomic system conditional to observing a given homodyne current trajectory, thus accounting for the competition between the Hamiltonian evolution and measurement back action. As an illustration, we discuss minimal models of atomic dynamics and continuous current measurement on rings with synthetic gauge fields, involving both real space and synthetic dimension lattices (represented by internal atomic states). Finally, by ``not reading'' the current measurements the time evolution of the atomic system is governed by a master equation, where---depending on the microscopic details of our CQED setups---we effectively engineer a current coupling of our system to a quantum reservoir. This provides interesting scenarios of dissipative dynamics generating ``dark'' pure quantum many-body states.
Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold Rydberg gases, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, nonequilibrium setting of cavity QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability, a foundational and patently nonequilibrium model of cavity QED, the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by making new connections between traditional techniques from many-body physics (functional integrals) and quantum optics (the system-size expansion). To lowest order in a controlled expansion---organized around the experimentally relevant limit of weak interactions---the full quantum dynamics reduces to nonequilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, revealing that canonical behavior associated with the Ising model manifests readily in simple experimental observables.
Pure quantum states, as described in quantum mechanics textbooks, are ideal representations inevitably deteriorated in real systems by any dissipative connection to the environment. In this work we derive a unified theoretical frame to study the non-Hermitian dynamics of a driven-dissipative quantum system and validate it by comparison to experimental data of matter-wave diffraction. To highlight the role of dissipation, we perform the comparison in a near-resonant regime of light-matter interaction, where perturbative approaches fail. Here, we show that the developed formalism enables both exact simulations and an intuitive interpretation based on modal analysis. The theoretical analysis is based on the general master equation description of driven-dissipative systems, from which we derive an effective complex potential Veff(Ω,Δ) that depends on control parameters such as the amplitude and detuning of the light matter interaction. Experimentally, we drive a 87Rb BEC near resonance using periodic excited-state engineering, mapping the spatially modulated Veff[Ω,Δ(x)] into momentum space for precise quantification. The experimental results agree with numerical simulations of the master equation and demonstrate the interplay between coherent drive and dissipation, with an exceptional signature: a reduced decay rate with increasing drive. Such dynamics is then interpreted by a modal analysis of the non-Hermitian Hamiltonian Heff=p2/2m+Veff which provide an intuitive and qualitative explanation for such driven-dissipative system.