Abstract In this work, we consider the feasibility of Schrödinger cat (SC) and N 00 N states formation by a convenient bosonic Josephson junction system in two-mode approximation. Starting with purely quantum description of two-mode Bose–Einstein condensate we investigate the effective potential approach that provides an accurate analytical description for the system with a large number of particles. We show that in the zero temperature limit SC states result from a quantum phase transition that occurs when the nonlinear strength becomes comparable with the Josephson coupling parameter. The Wigner function approach demonstrates the growth of the SC state halves separation and formation of N 00 N -like states (a Fock state superposition) with the particle number increase. We examine the possibility to attain the SC state at finite temperatures and a weak dissipation leading to appearing of some critical temperature; it defines the second-order phase transition from classical activation process to the SC state formation through the quantum tunneling phenomenon. Numerical estimations demonstrate that the critical temperature is sufficiently below the temperature of atomic condensation. The results obtained may be useful for experimental observation of SC states with small condensate Josephson junctions.
Abstract In this work, we consider the feasibility of Schrödinger cat (SC) and N 00 N states formation by a convenient bosonic Josephson junction system in two-mode approximation. Starting with purely quantum description of two-mode Bose–Einstein condensate we investigate the effective potential approach that provides an accurate analytical description for the system with a large number of particles. We show that in the zero temperature limit SC states result from a quantum phase transition that occurs when the nonlinear strength becomes comparable with the Josephson coupling parameter. The Wigner function approach demonstrates the growth of the SC state halves separation and formation of N 00 N -like states (a Fock state superposition) with the particle number increase. We examine the possibility to attain the SC state at finite temperatures and a weak dissipation leading to appearing of some critical temperature; it defines the second-order phase transition from classical activation process to the SC state formation through the quantum tunneling phenomenon. Numerical estimations demonstrate that the critical temperature is sufficiently below the temperature of atomic condensation. The results obtained may be useful for experimental observation of SC states with small condensate Josephson junctions.
We study the quantum behaviour of a binary mixture of Bose–Einstein condensates in a double-well potential starting from a two-mode Bose–Hubbard Hamiltonian. We focus on the small tunnelling amplitude regime and apply perturbation theory up to second order. Analytical expressions for the energy eigenvalues and eigenstates are obtained. Then, the quantum evolution of the number difference of bosons between the two potential wells is fully investigated for two different initial conditions: completely localized states and coherent spin states. In the first case both the short- and the long-time dynamics is studied and a rich behaviour is found, ranging from small amplitude oscillations and collapses and revivals to coherent tunnelling. In the second case, the short-timescale evolution of number difference is determined and a more irregular dynamics is evidenced. Finally, the formation of Schrödinger cat states is considered and shown to affect the momentum distribution.
We use the Bose-Hubbard Hamiltonian to study quantum fluctuations in canonical equilibrium ensembles of bosonic Josephson junctions at relatively high temperatures, comparing the results for finite particle numbers N to the classical limit that is attained as N approaches infinity. We consider both attractive and repulsive atom-atom interactions, with special focus on the behavior near the T=0 quantum phase transition that occurs, for large enough N, when attractive interactions surpass a critical level. Differences between Bose-Hubbard results for small N and those of the classical limit are quite small even when $N\ensuremath{\sim}100$, with deviations from the limit diminishing as 1/N.
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 behavior of the system is investigated at zero temperature by varying the interatomic interaction from the strongly attractive regime to the repulsive one. We show that the ground state exhibits a crossover from a macroscopic Schr\"odinger-cat state to a separable Fock state through an atomic coherent regime. By diagonalizing the Bose-Hubbard Hamiltonian we characterize the emergence of the macroscopic cat states by calculating the Fisher information F, the coherence by means of the visibility $\ensuremath{\alpha}$ of the interference fringes in the momentum distribution, and the quantum correlations by using the entanglement entropy S. Both Fisher information and visibility are shown to be related to the ground-state energy by employing the Hellmann-Feynman theorem. This result, together with a perturbative calculation of the ground-state energy, allows simple analytical formulas for F and $\ensuremath{\alpha}$ to be obtained over a range of interactions, in excellent agreement with the exact diagonalization of the Bose-Hubbard Hamiltonian. In the attractive regime the entanglement entropy attains values very close to its upper limit for a specific interaction strength lying in the region where coherence is lost and self-trapping sets in.
Abstract The Josephson junctions (JJs) are at the heart of modern quantum technologies and metrology. In this work we establish quantum features of an atomic soliton Josephson junction (SJJ) device, which consists of two weakly-coupled condensates with negative scattering length. The condensates are trapped in a double-well potential and elongated in one dimension. Starting with classical field theory we map for the first time a two-soliton problem onto the effective two-mode Hamiltonian and perform a second quantization procedure. Compared to the conventional bosonic Josephson junction condensate system, we show that the SJJ-model in quantum domain exhibits unusual features due to its effective nonlinear strength proportional to the square of total particle number, N 2. A novel self-tuning effect for the effective tunneling parameter is also demonstrated in the SJJ-model, which depends on the particle number and rapidly vanishes as the JJ population imbalance increases. The formation of entangled Fock state superposition is predicted for the quantum SJJ-model, revealing dominant N00N-state components at the ‘edges’ for n = 0, N particle number. We have shown that the obtained quantum state is more resistant to few particle losses from the condensates if tiny components of entangled Fock states are present in the vicinity of the major N00N-state component. This peculiarity of the quantum SJJ-model establishes an important difference from its semiclassical analogue obtained in the framework of Hartree approach. Our results are confirmed by studying the first and N-order Hillery–Zubairy criteria applied for studying multiparticle entanglement and planar spin squeezing. The Einstein–Podolsky–Rosen quantum steering represents an important prerequisite for the crossover to the mesoscopic superposition Schrödinger-cat and/or N00N-states. The feasibility in observation for these predicted states of the SJJ-model in the experiments is also discussed by taking into account one- and three-body losses for lithium condensates.
In this paper, we investigated theoretically the dynamic effect induced by nonlinear tunneling of two weakly linked Bose–Einstein condensates in an extended boson Josephson-junction model, in which the two-body interaction is extended to neighboring lattice sites in strong interaction regime. As a consequence the dynamic properties compared with the usual Josephson-junction model are crucially modified by the atom-pair tunneling, which leads to the macroscopic quantum-states of coherent relative-phase between two condensates seen to be effective Schrödinger cat states. The relative-phase is controllable by system parameters and thus can be used to realize the qubit in quantum computation.
We study the coherence fluctuations in a Josephson junction created by two weakly coupled Bose-Einstein condensates. We apply the two-mode approximation in the full quantum theory analysis, and so that the system is described by a two-site Bose-Hubbard Hamiltonian. The coherence fluctuations are determined by the total number of particles N, charging energy EC, junction energy EJ, asymmetry δ and temperature T. For zero-temperature symmetric systems, the coherence fluctuations increase with EC/EJ, however, the number squeezing increases with N2EC/EJ. For zero-temperature asymmetric systems, the coherence fluctuations are suppressed by the balance effects between asymmetry and interparticle interaction and the single-atom resonance effects. The coherence fluctuations grow with temperature, and the formation of a self-trapping state will cause abnormal behaviors at high temperatures.