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 the modes such that they are decoupled and one of them is left only with some one-photon population which can be observed upon its decay. We numerically find lower values of the second-order correlation function obtained at earlier times than with constant coupling, with larger one-photon populations and for longer time windows, corresponding thus to higher emission efficiency and easier detection. The presented methodology is not restricted to the system under study, but it can also be transferred to other related frameworks, to find the optimal driving fields which can improve the single-photon emission statistics from these systems.
We propose to generate photon-pair blockade in a Josephson-photonics circuit that consists of a dc voltage-biased Josephson junction in series with a superconducting charge qubit and two nondegenerate microwave resonators. The two-level charge qubit is utilized to create anticorrelations of the charge transport; that is, the simultaneous Cooper pair tunneling events are inhibited. When the Josephson frequency matches the sum of resonance frequencies of the charge qubit and the two resonators, we demonstrate that the two resonators can release their energies in the form of antibunched pairs of …
We introduce a dynamical blockade phenomenon occurring in a nonlinear bosonic mode induced by a combination of continuous and pulsed excitations. We find that the underlying mechanism for the blockade is general, enhancing antibunching in the strongly nonlinear regime and inducing it in the weakly nonlinear regime, without fine-tuning the system parameters. Moreover, this mechanism shows advantages over existing blockade mechanisms and is suitable for implementation in a wide variety of systems due to its simplicity and universality.
We study many-body quantum coherence and interaction blockade in two Josephson-linked Bose-Einstein condensates. We introduce universal operators for characterizing many-body coherence without limitations on the system symmetry and total particle number $N$. We reproduce the results for both coherence fluctuations and number squeezing in {\em symmetric} systems of large $N$, and reveal several peculiar phenomena that may occur in {\em asymmetric} systems and systems of small $N$. For asymmetric systems, we show that, due to an interplay between asymmetry and inter-particle interaction, the coh…
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 investigate the driven quantum phase transition between the oscillating motion and the classical nearly free rotations of the Josephson pendulum coupled to a harmonic oscillator in the presence of dissipation. We refer to this as the Josephson-Rabi model. This model describes the standard setup of circuit quantum electrodynamics, where typically a transmon device is embedded in a superconducting cavity. We find that by treating the system quantum mechanically this transition occurs at higher drive powers than expected from an all-classical treatment, which is a consequence of the quasiperio…
We study scattering of propagating microwave fields by a DC-voltage biased Josephson junction. At sub-gap voltages, a small Josephson junction works merely as a non-linear boundary that can absorb, amplify, and diversely convert propagating microwaves. In the leading-order perturbation theory of the Josephson coupling energy, the spectral density and quadrature fluctuations of scattered thermal and coherent radiation can be described in terms of the well-known $P(E)$ function. Applying this, we study how thermal and coherent radiation is absorbed and amplified in an Ohmic transmission line and…
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.
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 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…
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.
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 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.
The interaction blockade phenomenon isolates the motion of a single quantum particle within a multi-particle system, in particular for coherent oscillations in and out of a region affected by the blockade mechanism. For identical quantum particles with Bose statistics, the presence of the other particles is still felt by a bosonic stimulation factor $\sqrt{N}$ that speeds up the coherent oscillations, where $N$ is the number of bosons. Here we propose an experiment to observe this enhancement factor with a small number of bosonic atoms. The proposed protocol realises an asymmetric double well …
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…
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.
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 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 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 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 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 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.
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 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 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…
High quality factors, strong nonlinearities, and extensive design flexibility make superconducting circuits an ideal platform to investigate synchronization phenomena deep in the quantum regime. Recently~\cite{Loerch-2017}, it was predicted that energy quantization and conservation can block the synchronization of two identical, weakly coupled nonlinear self-oscillators. Here we propose a Josephson junction circuit realization of such a system along with a simple homodyne measurement scheme to observe this effect. We also show that at finite detuning, where phase synchronization takes place, t…
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…
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 …
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 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 …
We study coherent phonon oscillations and tunneling between two coupled nonlinear nanomechanical resonators. We show that the coupling between two nanomechanical resonators creates an effective phonon Josephson junction which exhibits two different dynamical behaviors: Josephson oscillation (phonon-Rabi oscillation) and macroscopic self-trapping (phonon blockade). Self-trapping originates from mechanical nonlinearities, meaning that when the nonlinearity exceeds its critical value, the energy exchange between the two resonators is suppressed, and phonon-Josephson oscillations between them are …
We analyze the ground-state properties of an artificial atom made out of repulsive bosons attracted to a center for the case that all the interactions are short-ranged. Such bosonic atoms could be created by optically trapping ultracold particles of alkali vapors; we present the theory describing how their properties depend on experimentally adjustable strength of ``nuclear'' attraction and interparticle repulsion. The binding ability of the short-range potential increases with space dimensionality - only a limited number of particles can be bound in one dimension, while in two and three dimen…
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…
We explore the interplay between tunneling and interatomic interactions in the dynamics of a bosonic Josephson junction. We tune the scattering length of an atomic $^{39}$K Bose-Einstein condensate confined in a double-well trap to investigate regimes inaccessible to other superconducting or superfluid systems. In the limit of small-amplitude oscillations, we study the transition from Rabi to plasma oscillations by crossing over from attractive to repulsive interatomic interactions. We observe a critical slowing down in the oscillation frequency by increasing the strength of an attractive inte…
Recent experimental demonstrations of quantum coherence of the charge and flux states of Josephson junctions show that the quantum Josephson dynamics can be used to develop scalable quantum logic circuits. In this work, I review the basic concepts of Josephson tunneling and Josephson-junction qubits, and discuss two problems of this tunneling motivated by quantum computing applications. One is the theory of photon-assisted resonant flux tunneling in SQUID systems used to demonstrate quantum coherence of flux. Another is the problem of quantum measurement of charge with the SET electrometer. It…
We investigate an atomic ensemble of interacting bosons trapped in a symmetric double well potential in contact with a single tightly trapped ion which has been recently proposed [R. Gerritsma et al., Phys. Rev. Lett. 109, 080402 (2012)] as a source of entanglement between a Bose-Einstein condensate and an ion. Compared to the previous study, the present work aims at performing a detailed and accurate many-body analysis of such combined atomic quantum system by means of the ab-initio multi-configuration time-dependent Hartree method for bosons, which allows to take into account all correlation…
We have theoretically investigated macroscopic quantum tunneling (MQT) and the influence of nodal quasiparticles and zero energy bound states (ZES) on MQT in s-wave/d-wave hybrid Josephson junctions. In contrast to d-wave/d-wave junctions, the low-energy quasiparticle dissipation resulting from nodal quasiparticles and ZES is suppressed due to a quasiparticle-tunneling blockade effect in an isotropic s-wave superconductor. Therefore, the inherent dissipation in these junctions is found to be weak. This result suggests high potential of s-wave/d-wave hybrid junctions for applications in quantum…
A dipolar condensate confined in a toroidal trap constitutes a self-induced Josepshon junction when the dipoles are oriented perpendicularly to the trap symmetry axis and the s-wave scattering length is small enough. The ring-shaped double-well potential coming from the anisotropic character of the mean-field dipolar interaction is robust enough to sustain self-trapping dynamics, which takes place when the initial population imbalance between the two wells is large. We show that in this system the self-trapping regime is directly related to a vortex-induced phase-slip dynamics. A vortex and an…
Measuring the quantum dynamics of a mechanical system, when few phonons are involved, remains a challenge. We show that a superconducting microwave resonator linearly coupled to the mechanical mode constitutes a very powerful probe for this scope. This new coupling can be much stronger than the usual radiation pressure interaction by adjusting a gate voltage. We focus on the detection of phonon blockade, showing that it can be observed by measuring the statistics of the light in the cavity. The underlying reason is the formation of an entangled state between the two resonators. Our scheme real…
We consider a bosonic Josephson junction made of $N$ ultracold and dilute atoms confined by a quasi one-dimensional double-well potential within the two-site Bose-Hubbard model framework. The behaviour of the system is investigated at zero temperature by varying the inter-atomic interaction from the strongly attractive regime to the repulsive one. We show that the ground-state exhibits a crossover from a macroscopic Schrödinger-cat state to a separable Fock state through an atomic coherent regime. By diagonalizing the Bose-Hubbard Hamiltonian we characterize the emergence of the mascroscopic c…
We revisit the dynamics of a Bose-Einstein condensate in a double-well potential, from the regime of Josephson plasma oscillations to the self-trapping regime, by means of the Bogoliubov quasiparticle projection method. For very small imbalance between left and right wells only the lowest Bogoliubov mode is significantly occupied. In this regime the system performs plasma oscillations at the corresponding frequency, and the evolution of the condensate is characterized by a periodic transfer of population between the ground and the first excited state. As the initial imbalance is increased, mor…
