We theoretically investigate the entanglement dynamics in photonic Mott insulators in the presence of particle losses and dephasing. We explore two configurations where entanglement is generated following the injection or extraction of a photon in the central site of a chain of cavity resonators. We study the entanglement negativity of two-site reduced density matrices as a function of time and inter-site distance. Our findings show that in spite of particle losses the quantum entanglement propagation exhibits a ballistic character with propagation speeds related to the differerent quasiparticles that are involved in the dynamics, namely photonic doublons and holons respectively. Our analysis reveals that photon dissipation has a strikingly asymmetric behavior in the two configurations with a much more dramatic role on the holon entanglement propagation than for the doublon case.
We show, that photon non-linearities in electromagnetically induced transparency can be at least one order of magnitude larger than predicted in all previous approaches. As an application we demonstrate that, in this regime they give rise to very strong photon - photon interactions which are strong enough to make an experimental realization of a photonic Mott insulator state feasible in arrays of coupled ultra high-Q micro-cavities.
The features of superfluid-Mott insulator phase transition in the array of dissipative cavities is analyzed. Employing a kind of quasi-boson and a mean-filed approach, we show analytically how dissipation and decoherence influence the critical behaviors and the time evolution of the system. We find that there is a localized tendency, which could lead to the break of superfluidity for a superfluid state and suppress the appearance of the long-range order form a Mott state. Eventually, a collection of mixture states localized on each site will arise.
Arrays of coupled photonic cavities driven by external lasers represent a highly controllable setup to explore photonic transport. In this paper we address (quasi)-steady states of this system that exhibit photonic currents introduced by engineering driving and dissipation. We investigate two approaches: in the first one, photonic currents arise as a consequence of a phase difference of applied lasers and in the second one, photons are injected locally and currents develop as they redistribute over the lattice. Effects of interactions are taken into account within a mean-field framework. In th…
We study the phenomenon of controllable localization-delocalization transition in a quantum many-body system composed of nitrogen-vacancy centers coupled to photonic crystal cavities, through tuning the different detunings and the relative amplitudes of two optical fields that drive two nondegenerate transitions of the $Λ$-type configuration. We not only characterize how dissipation affects the phase boundary using the mean-field quantum master equation, but also provide the possibility of observing this photonic quantum phase transition (QPT) by employing several experimentally observable qua…
As photons do not interact with each other, it is interesting to ask whether photonic systems can be modified to exhibit the phases characteristic of strongly coupled many-body systems. We demonstrate how a Mott insulator type of phase of excitations can arise in an array of coupled electromagnetic cavities, each of which is coupled resonantly to a {\em single} two level system (atom/quantum dot/Cooper pair) and can be individually addressed from outside. In the Mott phase each atom-cavity system has the same integral number of net polaritonic (atomic plus photonic) excitations with photon blo…
Superconducting circuits are a competitive platform for quantum computation because they offer controllability, long coherence times and strong interactions - properties that are essential for the study of quantum materials comprising microwave photons. However, intrinsic photon losses in these circuits hinder the realization of quantum many-body phases. Here we use superconducting circuits to explore strongly correlated quantum matter by building a Bose-Hubbard lattice for photons in the strongly interacting regime. We develop a versatile method for dissipative preparation of incompressible m…
We investigate the behavior of two coupled non-linear photonic cavities, in presence of inhomogeneous coherent driving and local dissipations. By solving numerically the quantum master equation, either by diagonalizing the Liouvillian superoperator or by using the approximated truncated Wigner approach, we extrapolate the properties of the system in a thermodynamic limit of large photon occupation. When the mean field Gross-Pitaevskii equation predicts a unique parametrically unstable steady-state solution, the open quantum many-body system presents highly non-classical properties and its dyna…
We study the dynamics of nonlinear photonic lattices driven by two-photon parametric processes. By means of matrix-product-state based calculations, we show that a quantum many-body state with long-range hidden order can be generated from the vacuum. This order resembles that characterizing the Haldane insulator. A possible explanation highlighting the role of the symmetry of the drive, and the effect of photon loss are discussed. An implementation based in superconducting circuits is proposed and analyzed
We propose a practical scheme to observe the polaritonic quantum phase transition (QPT) from the superfluid (SF) to Bose-glass (BG) to Mott-insulator (MI) states. The system consists of a two-dimensional array of photonic crystal microcavities doped with substitutional donor/acceptor impurities. Using realistic parameters, we show that such strongly correlated polaritonic systems can be constructed using the state-of-art semiconductor technology.
We theoretically study the dynamical Casimir effect (DCE), i.e., parametric amplification of a quantum vacuum, in an optomechanical cavity interacting with a photonic crystal, which is considered to be an ideal system to study the microscopic dissipation effect on the DCE. Starting from a total Hamiltonian including the photonic band system as well as the optomechanical cavity, we have derived an effective Floquet-Liouvillian by applying the Floquet method and Brillouin-Wigner-Feshbach projection method. The microscopic dissipation effect is rigorously taken into account in terms of the energy…
We propose an efficient numerical method to compute configuration averages of observables in disordered open quantum systems whose dynamics can be unraveled via stochastic trajectories. We prove that the optimal sampling of trajectories and disorder configurations is simply achieved by considering one random disorder configuration for each individual trajectory. As a first application, we exploit the present method to the study the role of disorder on the physics of the driven-dissipative Bose-Hubbard model in two different regimes: (i) for strong interactions, we explore the dissipative physi…
We experimentally perform the simulation of open quantum dynamics in single-qudit systems. Using a spatial light modulator as a dissipative optical device, we implement dissipative-dynamical maps onto qudits encoded in the transverse momentum of spontaneous parametric down-converted photon pairs. We show a well-controlled technique to prepare entangled qudits states as well as to implement dissipative local measurements; the latter realize two specific dynamics: dephasing and amplitude damping. Our work represents a new analogy-dynamical experiment for simulating an open quantum system.
We apply the Gaussian trajectories approach to the study of the critical behavior of two-dimensional dissipative arrays of nonlinear photonic cavities, in presence of two-photon driving and in regimes of sizable loss rates. In spite of the highly mixed character of the density matrix of this system, the numerical approach is able to provide precise estimations of the steady-state expectation values, even for large lattices made of more than 100 sites. By performing a finite-size scaling of the relevant properties of the steady state, we extrapolate the behavior of the system in the thermodynam…
The features of superfluid-Mott insulator phase transition in the array of dissipative nonlinear cavities are analyzed. We show analytically that the coupling to the bath can be reduced to renormalizing the eigenmodes of atom-cavity system. This gives rise to a localizing effect and drives the system into mixed states. For the superfluid state, a dynamical instability will lead to a sweeping to a localized state of photons. For the Mott state, a dissipation-induced fluctuation will suppress the restoring of long-range phase coherence driven by interaction.
Recent experimental advances enable the fabrication of photonic lattices in which the light propagates with non-trivial energy dispersions. When interfaced with quantum emitters, such systems yield strong collective spontaneous emission phenomena, such as perfect sub-radiance, in which the decay into the bath is completely suppressed, forming bound-states-in-the-continuum. Since such photonic lattices are generally lossy, an alternative way of probing them consists in coherently driving them to an steady-state from which photoluminescence can be extracted. Here, we formalize connections betwee…
Bosons hopping across sites and interacting on-site are the essence of the Bose-Hubbard model (BHM). Inspired by the success of BHM simulators with atoms in optical lattices, proposals for implementing the BHM with photons in coupled nonlinear cavities have emerged. Two coupled semiconductor microcavities constitute a model system where the hopping, interaction, and decay of exciton polaritons --- mixed light-matter quasiparticles --- can be engineered in combination with site-selective coherent driving to implement the driven-dissipative two-site optical BHM. Here we explore the interplay of …
Interferometric Readout of Momentum-Space Topology in a Programmable Dissipative Photonic Circuit
KTH Royal Institute of Technology（皇家理工学院）；Stockholm University（斯德哥尔摩大学）；Singapore University of Technology and Design（新加坡科技设计大学）；Huazhong University of Science and Technology（华中科技大学）
Photonic crystals provide an extremely powerful toolset for manipulation of optical dispersion and density of states, and have thus been employed for applications from photon generation to quantum sensing with NVs and atoms. The unique control afforded by these media make them a beautiful, if unexplored, playground for strong coupling quantum electrodynamics, where a single, highly nonlinear emitter hybridizes with the band structure of the crystal. In this work we demonstrate that such hybridization can create localized cavity modes that live within the photonic band-gap, whose localization a…
We propose the superfluid to Mott-insulator quantum phase transition in an array of exciton-polariton traps can be utilized for massive parallel generation of indistinguishable single photons. By means of analytical and numerical methods, the device operations and system properties are studied using realistic experimental parameters. Such a deterministic, fault-tolerant, massive parallel generation may open up a new perspective in photonic quantum information processing.
We propose a photonic quantum simulator for anti-ferromagnetic spin systems based on reservoir engineering. We consider a scheme where quadratically driven dissipative Kerr cavities are indirectly coupled via lossy ancillary cavities. We show that the ancillary cavities can produce an effective dissipative and Hamiltonian anti-ferromagnetic-like coupling between the cavities. By solving the master equation for a triangular cavity configuration, we demonstrate that the non-equilibrium steady state of the system bears full analogy with the ground state of an antiferromagnetic Ising model, exhibi…
We propose an optical simulation of dissipation-induced correlations in one-dimensional (1D) interacting bosonic systems, using a two-dimensional (2D) array of linear photonic waveguides and only classical light. We show that for the case of two bosons in a 1D lattice, one can simulate on-site two-body dissipative dynamics using a linear 2D waveguide array with lossy diagonal waveguides. The intensity distribution of the propagating light directly maps out the wave function, allowing one to observe the dissipation-induced correlations with simple measurements. Beyond the on-site model, we also…
We explore the dynamics of $N$ coupled atoms to a generic bosonic reservoir under specific system symmetries. In the regime of multiple atoms coupled to a single reservoir with identical couplings, we identify remarkable effects, notably that the initial configuration of the atomic excited state amplitudes strongly impacts the dynamics of the system and can even fully sever the system from its environment. Additionally, we find that steady state amplitudes of the excited states become independent of the choice of the reservoir. The framework introduced is applied to a structured photonic reser…
Coupled resonator arrays have been shown to exhibit interesting many- body physics including Mott and Fractional Hall states of photons. One of the main differences between these photonic quantum simulators and their cold atoms coun- terparts is in the dissipative nature of their photonic excitations. The natural equi- librium state is where there are no photons left in the cavity. Pumping the system with external drives is therefore necessary to compensate for the losses and realise non-trivial states. The external driving here can easily be tuned to be incoherent, coherent or fully quantum, …
Quantum key distribution (QKD) can distribute symmetric key bits between remote legitimate users with the guarantee of quantum mechanics principles. For practical applications, the compact and robust photonic components for QKD are essential, and there are increasing attention to integrate the source, detector and modulators on a photonic chip. However, the massive and parallel QKD based on wavelength multiplexing are still challenge, due to the limited coherent light sources on the chip. Here, we introduce the Kerr dissipative soliton in a microresonator, which provides the locked coherent fr…
Dynamical Casimir effect of the optomechanical cavity interacting with one-dimensional photonic crystal is theoretically investigated in terms of the complex spectral analysis of Floquet-Liouvillian in the symplectic-Floquet space. The quantum vacuum fluctuation of the intra-cavity mode is parametrically amplified by a periodic motion of the mirror boundary, and the amplified photons are spontaneously emitted to the photonic band. We have derived the non-Hermitian effective Floquet-Liouvillian from the total system Liouvillian with the use of the Brillouin-Wigner-Feshbach projection method in …
We demonstrate how the dissipative interaction between a superconducting qubit and a microwave photonic crystal can be used for quantum bath engineering. The photonic crystal is created with a step-impedance transmission line which suppresses and enhances the quantum spectral density of states, influencing decay transitions of a transmon circuit. The qubit interacts with the transmission line indirectly via dispersive coupling to a cavity. We characterize the photonic crystal density of states from both the unitary and dissipative dynamics of the qubit. When the qubit is driven, it dissipates …
By numerically calculating the time-evolved Wigner functions, we investigate the dynamics of a few-photon superposed (e.g., up to two ones) state in a dissipating cavity. It is shown that, the negativity of the Wigner function of the photonic state unquestionably vanishes with the cavity's dissipation. As a consequence, the nonclassical effects related to the negativity of the Wigner function should be weakened gradually. However, it is found that the value of the second-order correlation function $g^{(2)}(0)$ (which serves usually as the standard criterion of a typical nonclassical effect, i.…
To characterize the novel quantum phase transition for a hybrid system consisting of an array of coupled cavities and two-level atoms doped in each cavity, we study the atomic entanglement and photonic visibility in comparison with the quantum fluctuation of total excitations. Analytical and numerical simulation results show the happen of quantum critical phenomenon similar to the Mott insulator to superfluid transition. Here, the contour lines respectively representing the atomic entanglement, photonic visibility and excitation variance in the phase diagram are consistent in the vicinity of t…
We extend the idea of quantum phase transitions of light in the photonic Bose-Hubbard model with interactions to two atomic species by a self-consistent mean field theory. The excitation of two-level atoms interacting with coherent photon fields is analyzed with a finite temperature dependence of the order parameters. Four ground states of the system are found, including an isolated Mott-insulator phase and three different superfluid phases. Like two weakly coupled superconductors, our proposed dual-species lattice system shows a photonic analogue of Josephson effect. The dynamics of the propo…
An interesting problem in the field of quantum error correction involves finding a physical system that hosts a ``passively protected quantum memory,'' defined as an encoded qubit coupled to an environment that naturally wants to correct errors. To date, a quantum memory stable against finite-temperature effects is only known in four spatial dimensions or higher. Here, we take a different approach to realize a stable quantum memory by relying on a driven-dissipative environment. We propose a new model, the photonic-Ising model, which appears to passively correct against both bit-flip and phase…
We study the dissipative Fermi-Hubbard model in the limit of weak tunneling and strong repulsive interactions, where each lattice site is tunnel-coupled to a Markovian fermionic bath. For cold baths at intermediate chemical potentials, the Mott insulator property remains stable and we find a fast relaxation of the particle number towards half filling. On longer time scales, we find that the anti-ferromagnetic order of the Mott-Néel ground state on bi-partite lattices decays, even at zero temperature. For zero and non-zero temperatures, we quantify the different relaxation time scales by means …
We study photonic signatures of symmetry broken and topological phases in a driven, dissipative circuit QED realization of spin-1/2 chains. Specifically, we consider the transverse-field XY model and a dual model with 3-spin interactions. The former has a ferromagnetic and a paramagnetic phase, while the latter features, in addition, a symmetry protected topological phase. Using the method of third quantization, we calculate the non-equilibrium steady-state of the open spin chains for arbitrary system sizes and temperatures. We find that the bi-local correlation function of the spins at both e…
The nonclassical feature of photons in the open finite-size Dicke model is investigated via the two-photon correlation function. The quantum dressed master equation combined with the extended coherent photonic states is applied to analyze the dissipative dynamics of both the photons and qubits. The anti-bunching to bunching transition of photons is clearly observed by tuning the qubit-photon coupling strength. The optimal qubits number is unraveled to enhance the two-photon correlation function. Moreover, the temperature bias of thermal baths induces significant two-photon bunching signature w…
We explore theoretically the physics of dynamic hysteresis for driven-dissipative nonlinear photonic resonators. In the regime where the semiclassical mean-field theory predicts bistability, the exact steady-state density matrix is known to be unique, being a statistical mixture of two states: in particular, no static hysteresis cycle of the excited population occurs as a function of the driving intensity. Here, we predict that in the quantum regime a dynamic hysteresis with a rich phenomenology does appear when sweeping the driving amplitude in a finite time. The hysteresis area as a function…
Hybrid photonic-plasmonic nanostructures allow one to engineer coupling of quantum emitters and cavity modes accounting for the direct coherent and environment mediated dissipative pathways. Using generalized plasmonic Dicke model, we explore the non-equilibrium phase diagram with respect to these interactions. The analysis shows that their interplay results in the extension of the superradiant and regular lasing states to the dissipative coupling regime and an emergent lasing phase without population inversion having boundary with the superradiant and normal states. Calculated photon emission…
Based on tensor network realizations of path integrals reducing exponential memory scaling to polynomial efficiency and a Liouville space implementation of a time-discrete quantum memory, we investigate a quantum system simultaneously exposed to two structured reservoirs. For this purpose, we employ a numerically exact quasi-2D tensor network combining both diagonal and off-diagonal system-reservoir interactions with a twofold memory for continuous and discrete retardation effects. As a possible example, we study the non-Markovian dynamical interplay between discrete photonic feedback and stru…
Repulsive and attractive interactions usually lead to very different physics. Striking exceptions exist in the dynamics of driven-dissipative quantum systems. For the example of a photonic Bose-Hubbard dimer, we establish a one-to-one mapping relating the cases of onsite repulsion and attraction. We prove that the mapping is valid for an entire class of Markovian open quantum systems with time-reversal invariant Hamiltonian and physically meaningful inverse-sign Hamiltonian. To underline the broad applicability of the mapping, we illustrate the one-to-one correspondence between the nonequilibr…
We report a theoretical study of a quantum optical model consisting of an array of strongly nonlinear cavities incoherently pumped by an ensemble of population-inverted two-level atoms. Projective methods are used to eliminate the atomic dynamics and write a generalized master equation for the photonic degrees of freedom only, where the frequency-dependence of gain introduces non-Markovian features. In the simplest single cavity configuration, this pumping scheme gives novel optical bistability effects and allows for the selective generation of Fock states with a well-defined photon number. Fo…
We analyze an unusual class of bosonic dynamical instabilities that arise from dissipative (or non-Hermitian) pairing interactions. We show that, surprisingly, a completely stable dissipative pairing interaction can be combined with simple hopping or beam-splitter interactions (also stable) to generate instabilities. Further, we find that the dissipative steady state in such a situation remains completely pure up until the instability threshold (in clear distinction from standard parametric instabilities). These pairing-induced instabilities also exhibit an extremely pronounced sensitivity to …
We experimentally explore the dynamic optical hysteresis of a semiconductor microcavity as a function of the sweep time. The hysteresis area exhibits a double power law decay due to the shot noise of the driving laser, which triggers switching between metastable states. Upon increasing the average photon number and approaching the thermodynamic limit, the double power law evolves into a single power law. This algebraic behavior characterizes a dissipative phase transition. Our findings are in good agreement with theoretical predictions, and the present experimental approach is promising for th…
We study the driven-dissipative dynamics of photons interacting with an array of micromechanical membranes in an optical cavity. Periodic membrane driving and phonon creation result in an effective photon-number conserving non-unitary dynamics, which features a steady state with long-range photonic coherence. If the leakage of photons out of the cavity is counteracted by incoherent driving of the photonic modes, we show that the system undergoes a dynamical phase transition to the state with long-range coherence. A minimal system, composed of two micromechanical membranes in a cavity, is studi…
We theoretically show that the dynamics of a driven quantum harmonic oscillator subject to non-dissipative noise is formally equivalent to the single-particle dynamics propagating through an experimentally feasible dynamically-disordered photonic network. Using this correspondence, we find that noise assisted energy transport occurs in this network and, if the noise is Markovian or delta-correlated, we can obtain an analytical solution for the maximum amount of transferred energy between all network's sites at a fixed propagation distance. Beyond the Markovian limit, we further consider two di…
The embedding of tunable quantum emitters in a photonic bandgap structure enables the control of dissipative and dispersive interactions between emitters and their photonic bath. Operation in the transmission band, outside the gap, allows for studying waveguide quantum electrodynamics in the slow-light regime. Alternatively, tuning the emitter into the bandgap results in finite range emitter-emitter interactions via bound photonic states. Here we couple a transmon qubit to a superconducting metamaterial with a deep sub-wavelength lattice constant ($λ/60$). The metamaterial is formed by periodi…
We investigate two different kinds of quantum trajectories for a nonlinear photon resonator subject to two-photon pumping, a configuration recently studied for the generation of photonic Schroedinger cat states. In the absence of feedback control and in the strong-driving limit, the steady-state density matrix is a statistical mixture of two states with equal weight. While along a single photon-counting trajectory the systems intermittently switches between an odd and an even cat state, we show that upon homodyne detection the situation is different. Indeed, homodyne quantum trajectories revea…
