Shortcuts to adiabatic cat-state generation in bosonic Josephson junctions

Abstract

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 approaching the critical point, and the counter-diabatic driving in the ordered phase. Using the counter-diabatic driving, adiabatic generation of cat states is successfully accelerated. The enough large quantum Fisher information ensures that generated cat states are highly entangled. difficulty to find shortcuts depends on the sign of the nonlinear interaction. The ground state of the antiferromagnetic Lipkin-Meshkov-Glick model is the spin-squeezed Dicke state, which is unique and has been successfully produced using shortcuts to adiabaticity with high fidelity and within short time [77,79,81]. In contrast, the ground state of the ferromagnetic Lipkin-Meshkov-Glick model is the cat state. Shortcuts to adiabaticity in the ferromagnetic Lipkin-Meshkov-Glick model was first studied by Takahashi using the Holstein-Primakoff transformation in the thermodynamic limit [78]. Counter-diabatic driving was derived for both the disordered and the ordered phases. However, this counter-diabatic driving is ill-defined, i.e., diverges, at the critical point unless the fixed-point condition is satisfied. As discussed in literatures, especially in [80], this divergence is associated with the closing of the gap and the divergence of the correlation length. Campbell et al studied counter-diabatic driving around the critical point applying various approaches, especially in combination with optimal control [80]. By applying a small longitudinal field, which enables us to slightly avoid the critical point, mean-field prescription was applied both in the invariant-based inverse engineering approach [82] and the counter-diabatic driving approach [83].In this paper, we propose approximated counter-diabatic driving for bosonic Josephson junctions without energy imbalance, which is available across the critical point, using finite-size corrections in the Holstein-Primakoff transformation. Advantages of our method are that the counter-diabatic driving is well-defined over whole processes and that schedules of the counter-diabatic driving can be analytically obtained. Using our counter-diabatic driving, we can accelerate adiabatic generation of the cat state. Schedules of the counterdiabatic driving consist of three steps. The first one is the counter-diabatic driving in the disordered phase, where we aim to let the system be in the ground state. The second one is smoothly and slowly approaching the critical point, where we give up to be adiabatic but ai...

Focus on Shortcuts to Adiabaticity

“…The development of STA to control quantum correlations in multi-partite systems constitutes an important application in which progress has been somewhat restricted. Hatomura [91] addresses the preparation of catstates in bosonic Josephson junctions utilizing STA techniques. The analysis put forward relies on the description of the bosonic Josephson junction in terms of the semiclassical limit of the Lipkin-Meshkov-Glick model with a collective spin degree of freedom.…”

Superadiabatic generation of cat states in bosonic Josephson junctions under particle losses

“…For bimodal Bose-Einstein condensation, such additional terms counteracting diabatic changes were proposed [24]. The form of the additional Hamiltonian is nothing but the two-axis countertwisting (TACT) Hamiltonian [28].…”

“…Although realization of the TACT Hamiltonian is future work, one could question if the superadiabatic scheme based on shortcuts to adiabaticity [24] has any chance to work. In particular, particle losses, which take place due to collisions among atoms and always happen in ultracold atoms, cause various channels of decoherence and destroy macroscopic superpositions.…”

Maximizing entanglement in bosonic Josephson junctions using shortcuts to adiabaticity and optimal control

“…These include the fast cooling and transport of atoms [20,21], BECs [22] and trapped ions [23], the efficient manipulation of two-and three-level quantum systems [24,25], the design of waveguides and photonic lattices [26,27], the optimization of quantum heat engines [28][29][30][31][32][33], suppressing non-adiabatic excitations across a quantum phase transition [34,35], the fast optomechanical cooling [36] and quantum computation [37][38][39], and even the control of mechanical systems [40]. In the context of BJJs, STAs have been exploited for the fast generation of spin-squeezed states [41][42][43] and to expedite the superfluid to Mott-insulator transition [44,45].…”

“…We also express the desired transfer as an optimal control problem and use numerical optimization to obtain the controls which achieve it in minimum-time. Note that entanglement generation in BJJs is an active field of research for BECs trapped in optical lattices, with the emphasis given in the semiclassical limit of large occupation numbers [41][42][43][46][47][48][49][50]. Here on the contrary we consider the case of weak pumping, where the occupation numbers remain small.…”