We study the dynamics of a nonlinear dissipative bosonic Josephson junction (BJJ) with a time-dependent sinusoidal perturbation in interaction term. We demonstrate parametric resonance where the system undergoes sustained periodic oscillations even in the presence of dissipation. This happens when the frequency of the perturbation is close to twice the frequency of the unperturbed Josephson oscillations and the strength of perturbation exceeds a critical threshold. We have formulated the threshold conditions for parametric oscillations. To explore the nature of the oscillations, we carry out a multiple time scale analysis of the stability boundaries in terms of the V-shaped Arnold's tongue in the parameter space. Full numerical simulations have been performed for the zero-, running- and $π$-phase modes of nonlinear Josephson effect. Our results demonstrate that in $π$-phase mode, the system is capable of making a transition from regular parametric to chaotic parametric oscillations as one crosses the stability boundary. Also, the phase difference undergoes phase slip before executing sustained parametric oscillations.
We analyze Josephson's oscillation of Bose particles in the open (dissipative) Bose-Hubbard dimer. First, we excite the dimer from the vacuum state into a state suitable for observing the oscillation by using a special protocol for external driving. Next, we switch off the driving and observe the oscillation. It is shown that the main mechanism for the decay of Josephson's oscillation is the dephasing due to fluctuating number of particles in open systems. An analytical estimate for the decay time is obtained.
In this letter we propose a scheme for the preparation of steady entanglements in bosonic dissipative networks. We describe its implementation in a system of coupled cavities interacting with an engineered reservoir built up of three-level atoms. Emblematic bipartite ($Bell$ and $NOON$) and multipartite $W$-class states can be produced with high fidelity and purity.
We extend a recent method to shortcut the adiabatic following to internal bosonic Josephson junctions in which the control parameter is the linear coupling between the modes. The approach is based on the mapping between the two-site Bose-Hubbard Hamiltonian and a 1D effective Schrödinger-like equation, valid in the large $N$ (number of particles) limit. Our method can be readily implemented in current internal bosonic Josephson junctions and it improves substantially the production of spin-squeezing with respect to usually employed linear rampings.
Quantum dynamics of in-plane Josephson junctions between two d-wave superconducting films is described by the anisotropic XY-model where both, quasiparticle and Cooper pair tunneling terms, appear to be equally non-local. Applying a combination of the weak and strong coupling analyses to this model, we find a compelling evidence of a dissipative phase transition. The corresponding critical behavior is studied and contrasted with that found previously in the conventional (s-wave) Josephson junctions.
We theoretically investigate the properties of a double-well bosonic Josephson junction coupled to a single trapped ion. We find that the coupling between the wells can be controlled by the internal state of the ion, which can be used for studying mesoscopic entanglement between the two systems and to measure their interaction with high precision. As a particular example we consider a single $^{87}$Rb atom and a small Bose-Einstein condensate controlled by a single $^{171}$Yb$^+$ ion. We calculate inter-well coupling rates reaching hundreds of Hz, while the state dependence amounts to tens of …
We conceive an all-optical representation of the dynamics of two distinct types of interacting bosons in a double well by an array of evanescently coupled photonic waveguides. Many-particle interference effects are probed for various interaction strengths by changing the relative abundance of the particle species and can be readily identified by monitoring the propagation of the light intensity across the waveguide array. In particular, we show that finite inter-particle interaction strengths reduce the many-particle interference contrast by dephasing. A general description of the many-particl…
We describe a scheme with analytic result that allows to generate steady-state entanglement for two atoms over a dissipative bosonic medium. The resonant coupling between the mediating bosonic mode and cavity modes produces three collective atomic decay channels. This dissipative dynamics, together with the unitary process induced by classical microwave fields, drives the two atoms to the symmetric or asymmetric entangled steady state conditional upon the choice of the phases of the microwave fields. The effects on the steady-state entanglement of off-resonance mediating bosonic modes are anal…
We investigate the coherent dynamics of a non-interacting Bose-Einstein condensate in a system consisting of two bosonic reservoirs coupled via a spatially localized mode. We describe this system by a two-terminal Fano-Anderson model and investigate analytically the time evolution of observables such as the bosonic Josephson current. In doing so, we find that the Josephson current sensitively depends on the on-site energy of the localized mode. This facilitates to use this setup as a transistor for a Bose-Einstein condensate. We identify two regimes. In one regime, the system exhibits well-beh…
We calculate the out-of-time-ordered correlation function (OTOC) of a single impurity qubit coupled to fully a connected many-particle system such as a bosonic Josephson junction or spins with long-range interactions. In these systems the qubit OTOC can be used to detect both ground state and excited state quantum phase transitions (QPTs), making it a robust order parameter that is considerably more sensitive than the standard one-body correlation function. Finite size scaling exponents for an $N$ body system can also be accurately extracted from the long-time OTOC dynamics, however, for short…
We consider the standard double well setup extended with a laser beam in the center to create a "triple well" potential. The beam in the center is much more narrow than the barrier, and it creates a tunable depth well which can support a localized state in the middle. We show that the presence of the localized state in the central well changes the sign of tunneling between the left and right wells and therefore controls the fixed point dynamics of the bosonic Josephson junction.
In this article we consider a bosonic Josephson junction, a model system composed by two coupled nonlinear quantum oscillators which can be implemented in various physical contexts, initially prepared in a product of weakly populated coherent states. We quantify the maximum achievable entanglement between the modes of the junction and then use shortcuts to adiabaticity, a method developed to speed up adiabatic quantum dynamics, as well as numerical optimization, to find time-dependent controls (the nonlinearity and the coupling of the junction) which bring the system to a maximally entangled s…
We calculate the first two moments and full probability distribution of the work performed on a system of bosonic particles in a two-mode Bose-Hubbard Hamiltonian when the self-interaction term is varied instantaneously or with a finite-time ramp. In the instantaneous case, we show how the irreversible work scales differently depending on whether the system is driven to the Josephson or Fock regime of the bosonic Josephson junction. In the finite-time case, we use optimal control techniques to substantially decrease the irreversible work to negligible values. Our analysis can be implemented in…
We investigate a superadiabatic scheme to produce a cat state in a bosonic Josephson junction in absence and presence of particle losses. The generation scheme is based on shortcuts to adiabaticity and strongly relies on the parity conservation. The parity conservation also ensures that the produced state is a superposition of cat states with various sizes, i.e., a "cats state". Parity is also the quantity to be measured in order to utilize the produced state in interferometry. The generation scheme still works even if a number of particle losses during generation are substantial.
For the driven-dissipative system of two coupled bosonic modes in a nonlinear cavity resonator, we demonstrate a sequence of phase transitions from a trivial steady state to two distinct dissipative time crystalline phases. These effects are already anticipated at the level of the semiclassical analysis of the Lindblad equation using the theory of bifurcations and are further supported by the full quantum (numerical) treatment. The system is predicted to exhibit different dynamical phases characterized by an oscillating non-equilibrium steady state with non-trivial periodicity, which is a hall…
We present a method to perform a variational analysis of the quantum master equation for driven-disspative bosonic fields with arbitrary large occupation numbers. Our approach combines the P representation of the density matrix and the variational principle for open quantum system. We benchmark the method by comparing it to wave-function Monte-Carlo simulations and the solution of the Maxwell-Bloch equation for the Jaynes-Cummings model. Furthermore, we study a model describing Rydberg polaritons in a cavity field and introduce an additional set of variational paramaters to describe correlatio…
We propose a quantum speedup method for adiabatic generation of cat states in bosonic Josephson junctions via shortcuts to adiabaticity. We apply approximated counter-diabatic driving to a bosonic Josephson junction using the Holstein-Primakoff transformation. In order to avoid the problem of divergence in counter-diabatic driving, we take finite-size corrections into account. The resulting counter-diabatic driving is well-defined over whole processes. Schedules of the counter-diabatic driving consist of three steps; the counter-diabatic driving in the disordered phase, smoothly and slowly app…
Considering a network of dissipative quantum harmonic oscillators we deduce and analyze the optimum topologies which are able to store, for the largest period of time, a quantum superposition previously prepared in one of the network oscillators. The storage of the superposition is made dynamically, in that the state to be protected evolves through the network before being retrieved back in the oscillator where it was prepared. The decoherence time during the dynamic storage process is computed and we demonstrate that it is proportional to the number of oscillators in the network for a particu…
We analyze phase interferometry realized with a bosonic Josephson junction made of trapped dilute and ultracold atoms. By using a suitable phase sensitivity indicator we study the zero temperature junction states useful to achieve sub shot-noise precisions. Sub shot-noise phase shift sensitivities can be reached even at finite temperature under a suitable choice of the junction state. We infer a scaling law in terms of the size system (that is, the number of particles) for the temperature at which the shot-noise limit is not overcome anymore
We analyze the effects of the temperature on a bosonic Josephson junction realized with ultracold and dilute atoms in a double-well potential. Starting from the eigenstates of the two-site Bose-Hubbard Hamiltonian, we calculate the coherence visibility and the fluctuation of the on-site occupation number and study them as functions of the temperature. We show that, contrary to naive expectations, when the boson-boson interaction is suitably chosen thermal effects can increase the coherence visibility and reduce the on-site number fluctuation.
We present a detailed analysis of the relaxation dynamics in an extended bosonic Josephson junction. We show that stochastic classical field simulations using Gross-Pitaevskii equations in three spatial dimensions reproduce the main experimental findings of M. Pigneur et al., Phys. Rev. Lett. 120, 173601 (2018). We give an analytic solution describing the short time evolution through multimode dephasing. For longer times, the observed relaxation to a phase locked state is caused by nonlinear dynamics beyond the sine-Gordon model, induced by the longitudinal confinement potential and persisting…
We employ a semiclassical picture to study dynamics in a bosonic Josephson junction with various initial conditions. Phase-diffusion of coherent preparations in the Josephson regime is shown to depend on the initial relative phase between the two condensates. For initially incoherent condensates, we find a universal value for the buildup of coherence in the Josephson regime. In addition, we contrast two seemingly similar on-separatrix coherent preparations, finding striking differences in their convergence to classicality as the number of particles increases.
We use an exact quantum phase model to study the dynamical generation of particle-entanglement in a bosonic Josephson junction composed by two coupled and interacting Bose-Einstein condensates. Using analytical arguments, we show that linear coupling can accelerate the creation of entanglement with respect to the well known one-axis twisting model where coupling is absent. Furthermore, with a numerical analysis of optimal control schemes, we identify the optimal parameters for the fast generation of metrologically useful entanglement on short time scales: the optimal evolution is generated for…
We systematically study the influence of amplitude modulation on the steady-state bosonic squeezing and entanglement in a dissipative three-mode optomechanical system, where a vibrational mode of the membrane is coupled to the left and right cavity modes via the radiation pressure. Numerical simulation results show that the steady-state bosonic squeezing and entanglement can be significantly enhanced by periodically modulated external laser driving either or both ends of the cavity. Remarkably, the fact that as long as one periodically modulated external laser driving either end of the cavitie…
The quantum dynamics of a one-dimensional bosonic Josephson junction is studied by solving the time-dependent many-boson Schrödinger equation numerically exactly. Already for weak interparticle interactions and on short time scales, the commonly-employed mean-field and many-body methods are found to deviate substantially from the exact dynamics. The system exhibits rich many-body dynamics like enhanced tunneling and a novel equilibration phenomenon of the junction depending on the interaction, attributed to a quick loss of coherence.
We analyze an entangling protocol to generate tripartite Greenberger-Horne-Zeilinger states in a system consisting of three superconducting qubits with pairwise coupling. The dynamics of the open quantum system is investigated by taking into account the interaction of each qubit with an independent bosonic bath with an ohmic spectral structure. To this end a microscopic master equation is constructed and exactly solved. We find that the protocol here discussed is stable against decoherence and dissipation due to the presence of the external baths.
We present an analytical description of the tunneling dynamics between two coupled Bose-Einstein condensates in the Josephson regime. The model relies on the classical analogy with a rigid pendulum and focuses on two dynamical modes of this system: Josephson oscillations and Macroscopic Quantum Self-Trapping. The analogy is extended to include an energy difference between the two superfluids caused by an asymmetry in the trapping potential. The model is compatible with the mean-field predictions of the two-mode Bose-Hubbard model. It gives new insights on the mean-field model by involving expe…
We study suppression of nonadiabatic transitions during adiabatic generation of a cat-like state (a superposition of different size cat states) and a spin squeezed state in a bosonic Josephson junction. In order to minimize the adiabatic error, we use quantum adiabatic brachistochrone, which enables us to track a geometrically efficient path in parameter space under given conditions without requiring additional terms. For creation of a cat-like state, divergence of the quantum geometric tensor associated with gap closing at the critical point is avoided because of the parity conservation. The …
We analyze the emergence of Shapiro resonances in tunnel-coupled Bose-Einstein condensates, realizing a bosonic Josephson junction. Our analysis is based on an experimentally relevant implementation using magnetic double well potentials on an atomchip. In this configuration the potential bias (implementing the junction voltage) and the potential barrier (realizing the Josephson link) are intrinsically coupled. We show that the dynamically driven system exhibits significantly enhanced Shapiro resonances which will facilitate experimental observation. To describe the systems response to the dyna…
We theoretically study the phase dynamics in Josephson junctions, which maps onto the oscillatory motion of a point-like particle in the washboard potential. Under appropriate driving and damping conditions, the Josephson phase undergoes intriguing bistable dynamics near a saddle point in the quasienergy landscape. The bifurcation mechanism plays a critical role in superconducting quantum circuits with relevance to non-demolition measurements such as high-fidelity readout of qubit states. We address the question `what is the probability of capture into either basin of attraction' and answer it…
Half a century after its discovery, the Josephson junction has become the most important nonlinear quantum electronic component at our disposal. It has helped reshape the SI system around quantum effects and is used in scores of quantum devices. By itself, the use of Josephson junctions in the volt metrology seems to imply an exquisite understanding of the component in every aspect. Yet, surprisingly, there have been long-standing subtle issues regarding the modeling of the interaction of a junction with its electromagnetic environment. Here, we find that a Josephson junction connected to a re…
We study Floquet engineering of the tunnel coupling between a pair of one-dimensional bosonic quasi-condensates in a tilted double-well potential. By modulating the energy difference between the two wells, we re-establish tunnel coupling and precisely control its amplitude and phase. This allows us to initiate coherence between two initially uncorrelated Bose gases and prepare different initial states in the emerging sine-Gordon Hamiltonian. We fully characterize the Floquet system and study the dependence of both equilibrium properties and relaxation on the modulation.
Josephson effects are commonly studied in quantum systems in which dissipation or noise can be neglected or do not play a crucial role. In contrast, here we discuss a setup where dissipative interactions do amplify a photonic Josephson current, opening a doorway to dissipation-enhanced sensitivity of quantum-optical interferometry devices. In particular, we study two coupled nanolasers subjected to phase coherent drivings and coupled by a coherent photon tunneling process. We describe this system by means of a Fokker-Planck equation and show that it exhibits an interesting non-equilibrium phas…
We study the interplay between the dynamics of a Bose-Einstein condensate in a double-well potential and that of an optical cavity mode. The cavity field is superimposed to the double-well potential and affects the atomic tunneling processes. The cavity field is driven by a laser red detuned from the bare cavity resonance; the dynamically changing spatial distribution of the atoms can shift the cavity in and out of resonance. At resonance the photon number is hugely enhanced and the atomic tunneling becomes amplified. The Josephson junction equations are revisited and the phase diagram is calc…
The many-body Schrödinger dynamics of a one-dimensional bosonic Josephson junction is investigated for up to ten thousand bosons and long times. The initial states are fully condensed and the interaction strength is weak. We report on a universal fragmentation dynamics on the many-body level: systems consisting of different numbers of particles fragment to the same value at constant mean-field interaction strength. The phenomenon manifests itself in observables such as the correlation functions of the system. We explain this universal fragmentation dynamics analytically based on the Bose-Hubba…
We study the influence of photons on the dynamics and the ground state of the atoms in a Bosonic Josephson junction inside an optical resonator. The system is engineered in such a way that the atomic tunneling can be tuned by changing the number of photons in the cavity. In this setup the cavity photons are a new means of control, which can be utilized both in inducing self-trapping solutions and in driving the crossover of the ground state from an atomic coherent state to a Schrödinger's cat state. This is achieved, for suitable setup configurations, with interatomic interactions weaker than …
We present an experimental study on the non-equilibrium tunnel dynamics of two coupled one-dimensional Bose-Einstein quasi-condensates deep in the Josephson regime. Josephson oscillations are initiated by splitting a single one-dimensional condensate and imprinting a relative phase between the superfluids. Regardless of the initial state and experimental parameters, the dynamics of the relative phase and atom number imbalance shows a relaxation to a phase-locked steady state. The latter is characterized by a high phase coherence and reduced fluctuations with respect to the initial state. We pr…
We present a general approach to derive Lindblad master equations for a subsystem whose dynamics is coupled to dissipative bosonic modes. The derivation relies on a Schrieffer-Wolff transformation which allows to eliminate the bosonic degrees of freedom after self-consistently determining their state as a function of the coupled quantum system. We apply this formalism to the dissipative Dicke model and derive a Lindblad master equation for the atomic spins, which includes the coherent and dissipative interactions mediated by the bosonic mode. This master equation accurately predicts the Dicke …
We describe an apparatus designed to make non-demolition measurements on a Bose-Einstein condensate (BEC) trapped in a double-well optical cavity. This apparatus contains, as well as the bosonic gas and the trap, an optical cavity. We show how the interaction between the light and the atoms, under appropriate conditions, can allow for a weakly disturbing yet highly precise measurement of the population imbalance between the two wells and its variance. We show that the setting is well suited for the implementation of quantum-limited estimation strategies for the inference of the key parameters …
Typical treatments of superconducting or superfluid Josephson junctions rely on mean-field or two-mode models; we explore many-body dynamics of an isolated, ultracold, Bose-gas long Josephson junction using time-evolving block decimation simulations. We demonstrate that with increasing repulsive interaction strength, localized dynamics emerge that influence macroscopic condensate behavior and can lead to formation of solitons that directly oppose the symmetry of the junction. Initial state population and phase yield insight into dynamic tunneling regimes of a quasi one-dimensional double well …
Dissipative quantum phase transition has been widely believed to occur in a Josephson junction coupled to a resistor despite a lack of concrete experimental evidence. Here, on the basis of both numerical and analytical nonperturbative renormalization group (RG) analyses, we reveal breakdown of previous perturbative arguments and defy the common wisdom that the transition always occurs at the quantum resistance $R_{Q} \!=\! h/(4e^2)$. We find that RG flows in nonperturbative regimes induce nonmonotonic renormalization of the charging energy and lead to a qualitatively different phase diagram, w…
Asymptotic Entanglement across Dynamical Regimes of a Dissipative Bosonic Dimer
Peking University（北京大学）；Hefei National Laboratory（合肥国家实验室）；The Pennsylvania State University（宾夕法尼亚州立大学）；Beijing University of Posts and Telecommunications（北京邮电大学）；Shanxi University（山西大学）
We theoretically study the dipolar motion of bosonic atoms in a very shallow, strongly confined 1D optical lattice using the parameters of the recent experiment [Fertig et al., Phys. Rev. Lett. 94, 220402 (2005)]. We find that, due to momentum uncertainty, a small, but non-negligible, atom population occupies the unstable velocity region of the corresponding classical dynamics, resulting in the observed dissipative atom transport. This population is generated even in a static vapor, due to quantum fluctuations which are enhanced by the lattice and the confinement, and is not notably affected b…
In this article we use time-dependent Josephson coupling to enhance unconventional photon blockade in a system of two coupled nonlinear bosonic modes which are initially loaded with weakly populated coherent states, so the evolution is restricted to the manifold of up to two field quanta. Using numerical optimal control, we find the optimal coupling which minimizes the two-photon occupation of one mode, which is actually transferred to the other, while maintains a non-zero one-photon occupation in the same mode. Moreover, we choose the continuous coupling to vanish after the transfer between t…
The use of a Kerr nonlinearity to generate squeezed light is a well-known way to surpass the quantum noise limit along a given field quadrature. Nevertheless, in the most common regime of weak nonlinearity, a single Kerr resonator is unable to provide the proper interrelation between the field amplitude and squeezing required to induce a sizable deviation from Poissonian statistics. We demonstrate experimentally that weakly coupled bosonic modes allow exploration of the interplay between squeezing and displacement, which can give rise to strong deviations from the Poissonian statistics. In par…
We analyze the formation of squeezed states in a condensate of ultracold bosonic atoms confined by a double-well potential. The emphasis is set on the dynamical formation of such states from initially coherent many-body quantum states. Two cases are described: the squeezing formation in the evolution of the system around the stable point, and in the short time evolution in the vicinity of an unstable point. The latter is shown to produce highly squeezed states on very short times. On the basis of a semiclassical approximation to the Bose-Hubbard Hamiltonian, we are able to predict the amount o…
