Double-well Bose-Einstein Condensate Research Articles

Effect of time-dependent inter-particle interaction on the dynamics of a dissipative double-well Bose-Einstein condensate

Effect of time-dependent inter-particle interaction on the dynamics of a dissipative double-well Bose-Einstein condensate

Multi-pulse Ramsey interferometry of a double-well Bose–Einstein condensate in a cavity

Ramsey interferometry as one of the most important high-precision measurement methods has prospects for inferring various properties of ultracold atoms and molecules. We investigate the multi-pulse Ramsey interferometry of a double-well Bose–Einstein condensate (BEC) in an optical cavity. Compared with the standard two-pulse Ramsey scheme, our multi-pulse Ramsey proposal greatly relaxes the requirements for both intensity and width of the pulses, allowing the interferometry to be achieved using weak and narrow pulses. When the pumping pulses characterizing the coupling between the cavity field and the atomic BEC are applied to the zero background field, we demonstrate the atomic Ramsey fringes in the time domain for different pulse numbers and different pulse widths. We find that although the multi-pulse Ramsey fringes are no longer sensitive to cavity-pump detuning, they can still record the information of the interaction between coherent atoms. We obtain the fundamental frequency of the multi-pulse Ramsey fringes analytically and find that it is proportional to the number of pulses. Particularly, it is shown that the minimum of the fundamental frequency is exactly the critical point of the phase transition of the system. For a nonzero background field, the results indicate that a nondestructive observation of atomic Ramsey fringes by cavity transmission spectroscopy is feasible. Our findings provide insights for improving the accuracy of Ramsey interferometry and for using interferometry to observe phase transitions.

Noise-dissipation Correlated Dynamics of a Double-well Bose-Einstein Condensate-reservoir System

Abstract: In this work, we study the dissipative dynamics of a double-well Bose-Einstein condensate (BEC) out-coupled to reservoir at each side of its trap. The sub-system comprises of a simple Bose-Hubbard model, where the interplay of atom-tunneling current and inter-particle interaction are the main quantum features. The contact with two separate heat baths causes dissipation and drives the system into a non-equilibrium state. The system is well described by the Generalized Quantum Heisenberg-Langevin equation. We considered two Markovian dissipative BEC systems based on (i) the mean-field model (MF), where the internal noise has been averaged out and (ii) the noise-correlated model (FDT). Physical quantities, such as population imbalance, coherence and entanglement of the system, are computed for the models. The two-mode BEC phases, such as the quantum tunneling state and the macroscopic quantum-trapping state, evolved into complicated dynamics by controlling the non-linear interaction and dissipation strengths. We found that many important quantum features produced by the noise-correlated FDT model are not captured by the mean-field model. Keywords: Double-well BEC, Dissipation, Noise, Markovian, Non-Markovian, Fixed points. PACS: 03.75 Lm, 03.65 Yz, 03.75 Gg, 05.

Faraday-imaging-induced squeezing of a double-well Bose-Einstein condensate

We examine how nondestructive measurements generate spin squeezing in an atomic Bose-Einstein condensate confined in a double-well trap. The condensate in each well is monitored using coherent light beams in a Mach-Zehnder configuration that interacts with the atoms through a quantum nondemolition Hamiltonian. We solve the dynamics of the light-atom system using an exact wave-function approach, in the presence of dephasing noise, which allows us to examine arbitrary interaction times and a general initial state. We find that monitoring the condensate at zero detection current and with identical coherent light beams minimizes the backaction of the measurement on the atoms. In the weak atom-light interaction regime, we find the mean spin direction is relatively unaffected, while the variance of the spins is squeezed along the axis coupled to the light. Additionally, squeezing persists in the presence of tunneling and dephasing noise. For long atom-light interaction time, we equally show our methods can be used to prepare non-Gaussian correlated spin states.

On a mathematical model for a damped and driven double-well Bose–Einstein condensate

In this paper we consider a two-mode dynamical system as a model for a driven one-dimensional damped Bose–Einstein condensate in a double-well trapping potential. In the case of a constant external driving force the existence and stability of stationary solutions are discussed in relation to the values of the physical parameters. In the case of a time-dependent periodic external driving force the existence of limit cycles is proved, and the amplitude of these limit cycles exhibits a jump phenomenon for critical values of the physical parameters.

Non-linear Dynamics of a Double-Well Bose–Einstein Condensate–Reservoirs System

We investigate the dynamics of a Bose–Einstein condensate (BEC) confined within a symmetric double-well trap out-coupled to reservoirs. Our model is based on the quantum Heisenberg–Langevin approach. Dissipation in the system is induced by the interaction of condensate bosons with the reservoir which determines the Markovian and non-Markovian operational dynamics. These distinct dynamics correspond directly to the choice of function used in the dissipation kernel of the quantum Langevin equation. The main focus of this work is to study non-Markovian dynamics of the system proliferated by the use of Ornstein–Uhlenbeck (OU) memory function. Comparison is made with the Markovian dynamics induced by the use of δ-memory-less function. We have calculated numerically the time evolution of population imbalance and tunneling current of the system and found dissipation destroys the regular pattern of the two-mode BEC phases. Comparison between dissipative models shows significant differences in their dynamics, particularly in the strongly interacting case.

Estimation of entanglement in bipartite systems directly from tomograms

We investigate the advantages of extracting the degree of entanglement in bipartite systems directly from tomograms, as it is the latter that are readily obtained from experiments. This would provide a superior alternative to the standard procedure of assessing the extent of entanglement between subsystems after employing the machinery of state reconstruction from the tomogram. The latter is both cumbersome and involves statistical methods, while a direct inference about entanglement from the tomogram circumvents these limitations. In an earlier paper, we had identified a procedure to obtain a bipartite entanglement indicator directly from tomograms. To assess the efficacy of this indicator, we now carry out a detailed investigation using two nonlinear bipartite models by comparing this tomographic indicator with standard markers of entanglement such as the subsystem linear entropy and the subsystem von Neumann entropy and also with a commonly-used indicator obtained from inverse participation ratios. The two model systems selected for this purpose are a multilevel atom interacting with a radiation field, and a double-well Bose-Einstein condensate. The role played by the specific initial states of these two systems in the performance of the tomographic indicator is also examined. Further, the efficiency of the tomographic entanglement indicator during the dynamical evolution of the system is assessed from a time-series analysis of the difference between this indicator and the subsystem von Neumann entropy.

Symmetry-Broken Many-Body Excited States of the Gaseous Atomic Double-Well Bose-Einstein Condensate.

Macroscopic, many-body self-trapped and quantum superposition states of the gaseous double-well Bose-Einstein condensate (BEC) are investigated within the context of a multiconfigurational bosonic self-consistent field theory based upon underlying spatially symmetry-broken one-body wave functions. To aid in the interpretation of our results, an approximate model is constructed in the extreme Fock state limit, in which self-trapped and superposition states emerge in the many-body spectrum, striking a delicate balance between the degree of symmetry breaking, the effects of the condensate's mean field, and that of atomic correlation. It is found, in both the model and full theory, that the superposition state lies energetically below its related self-trapped counterpart even when many configurations are involved. Noticeably different spatial density profiles are associated with each type of excited state, thus providing a rigorous justification for approximate descriptions of high-lying excited states of the BEC.

Leggett-Garg tests of macrorealism for bosonic systems including double-well Bose-Einstein condensates and atom interferometers

We construct quantifiable generalizations of Leggett-Garg tests for macro- and mesoscopic realism and noninvasive measurability that apply when not all outcomes of measurement can be identified as arising from one of two macroscopically distinguishable states. We show how quantum mechanics predicts a negation of the Leggett-Garg premises for strategies involving ideal negative-result, weak, and minimally invasive (``nonclumsy'') projective measurements on dynamical entangled systems, as might be realized with Bose-Einstein condensates in a double-well potential, path-entangled NOON states, and atom interferometers. Potential loopholes associated with each strategy are discussed.

Interaction-modulated tunneling dynamics in a mixture of Bose–Einstein condensates

We study the interaction-modulated tunneling dynamics of a Bose-Einstein condensate (BEC) in a deep double-well potential, where the tunneling between the two wells is modulated by another BEC trapped in a harmonic potential symmetrically positioned at the center of the double-well potential. The inter-species interactions couple the dynamics of the two BECs, which give rise to interesting features in the tunneling oscillations. Adopting a two-mode approximation for the BEC in the double-well potential and coupling it with the Gross-Pitaevskii equation of the harmonically trapped BEC, we numerically investigate the coupled dynamics of the BEC mixture, and map out the phase diagram of the tunneling dynamics. We show that the dynamical back action of the BEC in the harmonic trap leads to strong non-linearity in the oscillations of the BEC in the double-well potential, which enriches the system dynamics, and enhances macroscopic self trapping. The transition between the Josephson oscillation and the self-trapping dynamics can be identified by monitoring the oscillation frequency of the double-well BEC. Our results suggest the possibility of tuning the tunneling dynamics of BECs in double-well potentials.

Signatures of nonclassical effects in optical tomograms

Several nonclassical effects displayed by wave packets governed by nonlinear Hamiltonians can be identified and assessed directly from tomograms without attempting to reconstruct the Wigner function or the density matrix explicitly. We have demonstrated this for both single-mode and bipartite systems. We have shown that a wide spectrum of effects such as the revival phenomena, quadrature squeezing, and Hong–Mandel and Hillery type higher-order squeezing in a generic single-mode system and the double-well Bose–Einstein condensate (BEC) can be obtained from appropriate tomograms in a straightforward manner. We have examined the manner in which decoherence affects the nature of the state of a generic single-mode system at specific instants during temporal evolution. We have investigated entropic squeezing of the subsystem state of a bipartite system as it evolves in time, solely from tomograms. The procedures that we have demonstrated can be readily adapted to multimode systems. Further, for the double-well BEC we have identified an indicator of entanglement between subsystems that can be obtained directly from the tomogram. This mirrors the qualitative behavior of the subsystem von Neumann entropy and the subsystem linear entropy.

Experimental Demonstration of Spontaneous Chirality in a Nonlinear Microresonator.

Chirality is an asymmetric property widely found in nature. Here, we propose and demonstrate experimentally the spontaneous emergence of chirality in an on-chip ultrahigh-Q whispering-gallery microresonator, without broken parity or time-reversal symmetry. This counterintuitive effect arises due to the inherent Kerr-nonlinearity-modulated coupling between clockwise and counterclockwise propagating waves. Above an input threshold of a few hundred microwatts, the initial chiral symmetry is broken spontaneously, and the counterpropagating output ratio exceeds 20∶1 with bidirectional inputs. The spontaneous chirality in an on-chip microresonator holds great potential in studies of fundamental physics and applied photonic devices.

Dynamics of the double-well Bose–Einstein condensate coupled to a dual Markovian reservoirs system

The dynamics of atomic condensate loaded in a double-well symmetric traps coupled to distinct dual reservoirs is studied. The effect of damping on the population evolution through the exposure of traps to their respective reservoir has been analysed at various temperatures. Damping in our system is induced by the fluctuation of the reservoir in agreement with the fluctuation–dissipation theorem. We found damping due to strong reservoir correlation destroy the quantum tunnelling state and macroscopic quantum self-trap state of the closed two-mode Bose–Einstein condensate states at all finite temperatures. Alternatively switching the trap’s out-coupling damping rates shows significant change in the population dynamics particularly in the strongly interacting case. Dissipation coupled with strong on-site interaction in the traps exhibits even more interesting dynamics as the equilibrium temperature in system is increased.

Realizing -symmetric BEC subsystems in closed Hermitian systems

In open double-well Bose–Einstein condensate systems which balance in- and outfluxes of atoms and which are effectively described by a non-Hermitian -symmetric Hamiltonian -symmetric states have been shown to exist. -symmetric states obey the combined parity and time reversal symmetry. We tackle the question of how the in- and outfluxes can be realized and introduce a Hermitian system in which two -symmetric subsystems are embedded. This system no longer requires an in- and outcoupling to and from the environment. We show that the subsystems still have -symmetric states. In addition we examine what degree of detail is necessary to correctly model the -symmetric properties and the bifurcation structure of such a system. We examine a four-mode matrix model and a system described by the full Gross–Pitaevskii equation in one dimension. We see that a simple matrix model correctly describes the qualitative properties of the system. For sufficiently isolated wells there is also quantitative agreement with the more advanced system descriptions. We also investigate which properties the wave functions of a system must fulfil to allow for -symmetric states. In particular the requirements for the phase difference between different parts of the system are examined.

Dissipation effect in the double-well Bose-Einstein condensate

Dynamics of the double-well Bose-Einstein condensate subject to energy dissipation is studied by solving a reduced one-dimensional time-dependent Gross-Pitaevskii equation numerically. We first reproduce the phase space diagram of the system without dissipation systematically, and then calculate evolutionary trajectories of dissipated systems. It is clearly shown that the dissipation can drive the system to evolve gradually from the π-mode quantum macroscopic self-trapping state, a state with relatively higher energy, to the lowest energy stationary state in which particles distribute equally in the two wells. The average phase and phase distribution in each well are discussed as well. We show that the phase distribution varies slowly in each well but may exhibit abrupt changes near the barrier. This sudden change occurs at the minimum position in particle density profile. We also note that the average phase in each well varies much faster with time than the phase difference between two wells.

Macroscopic Quantum Self-Trapping in Dynamical Tunneling

It is well known that increasing the nonlinearity due to repulsive atomic interactions in a double-well Bose-Einstein condensate suppresses quantum tunneling between the two sites. Here we find analogous behavior in the dynamical tunneling of a Bose-Einstein condensate between period-one resonances in a single driven potential well. For small nonlinearities we find unhindered tunneling between the resonances, but with an increasing period as compared to the noninteracting system. For nonlinearities above a critical value we generally observe that the tunneling shuts down. However, for certain regimes of modulation parameters we find that dynamical tunneling reemerges for large enough nonlinearities, an effect not present in spatial double-well tunneling. We develop a two-mode model in good agreement with full numerical simulations over a wide range of parameters, which allows the suppression of tunneling to be attributed to macroscopic quantum self-trapping.

QUANTUM CORRECTIONS TO THE DYNAMICS OF THE BOSE–EINSTEIN CONDENSATE IN A DOUBLE-WELL POTENTIAL

The dynamics of the Bose–Einstein condensate (BEC) in a double-well potential is often investigated under the mean-field theory (MFT). This works successfully for large particle numbers with dynamical stability. But for dynamical instabilities, quantum corrections to the MFT becomes important [J. R. Anglin and A. Vardi, Phys. Rev. A64, 013605 (2001)]. Recently the adiabatic dynamics of the double-well BEC is investigated under the MFT in terms of a dark variable [C. Ottaviani et al., Phys. Rev. A81, 043621 (2010)], which generalizes the adiabatic passage techniques in quantum optics to the nonlinear matter-wave case. We give a fully quantized version of it using second-quantization and introduce new correction terms from higher order interactions beyond the on-site interaction, which are interactions between the tunneling particle and the particle in the well and interactions between the tunneling particles. If only the on-site interaction is considered, this reduces to the usual two-mode BEC.

Steady-state entanglement in a double-well Bose-Einstein condensate through coupling to a superconducting resonator

We consider a two-component Bose-Einstein condensate in a double-well potential, where the atoms are magnetically coupled to a single-mode of the microwave field inside a superconducting resonator. We find that the system has the different dark-state subspaces in the strong- and weak-tunneling regimes, respectively. In the limit of weak tunnel coupling, steady-state entanglement between the two spatially separated condensates can be generated by evolving to a mixture of dark states via the dissipation of the photon field. We show that the entanglement can be faithfully indicated by an entanglement witness. Long-lived entangled states are useful for quantum information processing with atom-chip devices.

Creating Nonclassical States of Bose-Einstein Condensates by Dephasing Collisions

We show, using an exactly solvable model, that nonlinear dynamics is induced in a double-well Bose-Einstein condensate (BEC) by collisions with a thermal reservoir. This dynamics can facilitate the creation of phase or number squeezing and, at longer times, the creation of macroscopic nonclassical superposition states. Enhancement of these effects is possible by loading the reservoir atoms into an optical lattice.

Multimode analysis of non-classical correlations in double-well Bose–Einstein condensates

The observation of non-classical correlations arising in two weakly coupled Bose–Einstein condensates was recently reported by Estève et al (2008 Nature 455 1216). In order to observe relative number fluctuations between the two condensates below the standard quantum limit, they utilized the process of ‘adiabatic passage’ to drive the system out of thermal equilibrium. They found that this reduced the relative number fluctuations below that expected in thermal equilibrium at the minimum experimentally realizable temperature. We present a theoretical analysis that takes into account the spatial degrees of freedom of the system, allowing us to calculate the expected correlations at finite temperature in the system, and to verify the hypothesis of reduced number fluctuations via adiabatic passage by comparing the dynamics to the idealized model.