Mesoscopic quantum superposition states of weakly-coupled matter-wave solitons

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 doublewell 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 (BJJ) 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 N 00N-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 N 00N-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 (EPR) quantum steering represents an important prerequisite for the crossover to the mesoscopic superposition Schrödinger-cat and/or N 00N-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.

Bose-Einstein Condensate Soliton Qubit States for Metrological Applications

“…From the experimental point of view, the recent BEC soliton experiments with lithium condensates demonstrated that collisions may be recognized as one of the most detrimental effects 34 . However, as we established in 37 , the three-body and one-body losses may be unimportant at the time scales of few tens of milliseconds, which is relevant to experimental conditions in 34 . Moreover, the purely quantum analysis of the problem demonstrated that the superposition of Fock states, occurring at some specific parameters of the system, behaves robust to few particle losses.…”

“…1. Previously, in 37 , we examined this problem for quantum solitons possessing simple Josephson coupling. From the experimental point of view, the recent BEC soliton experiments with lithium condensates demonstrated that collisions may be recognized as one of the most detrimental effects 34 .…”

“…We start with the mean-field description of coupled mode-theory approach to an elongated BEC trapped in V = V H +V (x) potential, where V H is a 3D harmonic trapping potential; while V (x) is responsible for the double-well confinement in one (X) dimension 37 . The (rescaled) condensate wave function (mean field amplitude) Ψ(x) obeys the familiar 1D Gross-Pitaevskii equation (GPE), cf.…”

“…Atomic gap solitons are also observed in condensates with repulsive inter-particle interaction 31 . Based on soliton modes, we recently proposed the quantum soliton Josephson junction (SJJ) device with the novel concept to improve the quantum properties of the effectively coupled two-mode system [35][36][37] . The SJJ-device consists of two weakly-coupled condensates trapped in a double-well potential and elongated in one dimension.…”

“…In the framework of nonlinear quantum metrology, we also showed that solitons permit a Super-Heisenberg (SH) scaling (∝ N −3/2 ) even with coherent probes 36 . On the other hand, steady-states of coupled solitons can be useful for effective formation of Schrödinger-cat (SC) superposition state and maximally path-entangled N00N-states, which can be applied for the phase estimation purposes 37 . It is important that such superposition states arise only for soliton-shape condensate wave functions and occur due to the existence of certain steady-states in the phase difference -population imbalance phase plane 36 .…”