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Communications in Theoretical Physics

Design of shortcuts to adiabaticity for Bose–Einstein condensate dynamics in soliton Josephson junctions

Jingru Wu, Chengyu Han, Qian Kong

Published Jul 2, 2024• 2 citations
Publisher

Abstract

Abstract This article primarily establishes a two-soliton system and employs the Lewis–Riesenfeld invariant inverse control method to achieve shortcuts to adiabaticity (STA) technology. We study an atomic soliton Josephson junctions (SJJs) device and subsequently compare and analyze it with atomic bosonic Josephson junctions. Moreover, we use higher-order expressions of the auxiliary equations to optimize the results and weaken the detrimental effect of the sloshing amplitude. We find that in the adiabatic shortcut evolution of two systems with time-containing tunnelling rates, the SJJs system is more robust over a rather short time evolution. In comparison with linear ramping, the STA technique is easier to achieve with the precise modulation of the quantum state in the SJJs system.

DOI
10.1088/1572-9494/ad5d8f

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Abstract This article primarily establishes a two-soliton system and employs the Lewis–Riesenfeld invariant inverse control method to achieve shortcuts to adiabaticity (STA) technology. We study an atomic soliton Josephson junctions (SJJs) device and subsequently compare and analyze it with atomic bosonic Josephson junctions. Moreover, we use higher-order expressions of the auxiliary equations to optimize the results and weaken the detrimental effect of the sloshing amplitude. We find that in the adiabatic shortcut evolution of two systems with time-containing tunnelling rates, the SJJs system is more robust over a rather short time evolution. In comparison with linear ramping, the STA technique is easier to achieve with the precise modulation of the quantum state in the SJJs system.
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 one-dimensional effective Schr\"odinger-like equation, valid in the large-NNN (number of particles) limit. Our method can be readily implemented in current internal bosonic Josephson junctions and it substantially improves the production of spin squeezing with respect to the usually employed linear rampings.
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 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 state.
In general, the conventional Lewis-Riesenfeld invariant-based inverse engineering is a nonadiabatic process that results in the adiabatic final states to achieve the shortcut to adiabaticity, which does not provide complete suppression of non-adiabaticity throughout the evolution. We propose a new method to accomplish the shortcut to adiabaticity through an entirely adiabatic path. This new method is developed using the number operator as an invariant of the Hamiltonian. This paper discusses the mathematical framework of the new method in two-level quantum system and analyzes its performance compared to the conventional Lewis-Riesenfeld invariant-based inverse engineering method.
Adiabatic processes in quantum mechanics are very useful to prepare and manipulate quantum states but have the drawback of requiring long operation times. Hence there is a long time for the system to interact with its environment which can lead to a loss of coherence of the final state. This decoherence is problematic for implementing future quantum technologies which require the state's quantum mechanical features. “Shortcuts to Adiabaticity"(STA) provides a toolbox of methods to improve on adiabatic processes. Using these methods one can derive alternative processes which work for much shorter times with perfect fidelity. Since adiabatic processes are ubiquitous in atomic, molecular and optical physics, there is a broad scope of application for STA. In this thesis, STA (especially those using Lewis-Riesenfeld invariants) are applied to a variety of quantum systems for the purpose of quantum state transfer. In particular I show that STA control schemes in two- and three-level systems can be optimised to be more stable against unwanted uncontrollable transitions than adiabatic methods with the same operation time. I also show that STA methods can be applied in a triple well ring system with complex tunnelling, in optical lattices for the purposes of generating a higher orbital state of neutral atoms and in Penning traps to quickly compress or expand the trapped ion wavefunction. Finally I also investigate the effect of classical Poisson white noise on adiabatic processes.
Shortcuts to adiabaticity, originally developed in the context of quantum control, are powerful tools for the design of high coupling efficiency, robust, and short coupled-waveguide devices. The counterdiabatic protocol cancels the unwanted coupling in system evolution by the addition of a counterdiabatic term. The invariant-based inverse-engineering approach designs system evolution using the decoupled eigenstates of the Lewis-Riesenfeld invariant. The single-shot shaped-pulse technique directly parameterizes the solution of the coupled-mode equation. Starting from the counterdiabatic protocol, we show that these seemingly very different shortcuts to adiabaticity techniques are equivalent in the framework of coupled-waveguide systems. When combined with perturbation treatment of the coupled-mode equation, robust coupled-waveguide devices against errors can be obtained.