Shortcut to Adiabaticity for an Anisotropic Gas Containing Quantum Defects

Abstract

We present a Shortcut To Adiabaticity (STA) protocol applicable to 3D unitary Fermi gases and 2D weakly-interacting Bose gases containing defects such as vortices or solitons. Our protocol relies on a new class of exact scaling solutions in the presence of anisotropic time-dependent harmonic traps. It connects stationary states in initial and final traps having the same frequency ratios. The resulting scaling laws exhibit a universal form and also apply to the classical Boltzmann gas. The duration of the STA can be made very short so as to realize a quantum quench from one stationary state to another. When applied to an anisotropically trapped superfluid gas, the STA conserves the shape of the quantum defects hosted by the cloud, thereby acting like a perfect microscope, which sharply constrasts with their strong distortion occurring during the free expansion of the cloud. Solitons and quantized vortices are fundamental excitations of non-linear media and play a key role in superfluid dynamics [1]. In anisotropic geometries, the energetically favored defects are solitonic vortices, characterized by a non-circular velocity field which nevertheless presents non-zero circulation [2,3]. The investigation of their dynamics has been initiated by recent experiments where they were created either deterministically by phase imprinting [4], or spontaneously in a system which is quickly driven through a phase transition [5]. These defects exhibit intricate dynamics and decay mechanisms. For example, the snake instability [6], which affects solitons in 2D and in 3D, can lead to the creation of a solitonic vortex, a process which is likely to have played a role in [7]. The size of these defects is set by the healing length [8, chap. 5], which is too small to allow for in-situ observation. Up to now they have always been observed after the free expansion of the cloud, which increases the core dimensions. However, in the anisotropic case, the free expansion strongly distorts the cloud, and its use in the presence of a solitonic vortex leads to an involved density profile sporting a twisted nodal line [9].An alternative to free expansion is provided by the recent Shortcut To Adiabaticity (STA) schemes [10,11], which reversibly evolve a many-body system from one state to another, reaching the same target state as an adiabatic transformation in a much shorter time over which decoherence and losses are minimal. They allow for the manipulation of the momentum spread of a wavepacket without the time constraints of delta kick cooling [12,13]. They can be formulated as counterdiabatic driving [14,15]. They are being considered for the preparation of many-body states [16][17][18], they have motivated an exploration of the quantum speed limit [19] and reflection on the third law of thermodynamics [20].The construction of an STA relies on the existence of a scaling solution to the equation describing the manybody dynamics of the system in a time-dependent trap. Such a solution exists for the ideal gas in a harmonic trap and has been used...

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