Maximum work in minimum time from a conservative quantum system

Abstract

This paper considers the problem of obtaining maximum work from a conservative quantum system corresponding to a given change in an external parameter in the Hamiltonian. The example we present is a non-interacting collection of harmonic oscillators with a shared frequency omega which changes from a given initial to a given final value. The example is interesting for its role in experiments at ultra-low temperatures and for probing finite-time versions of the third law of thermodynamics. It is also the simplest system displaying quantum friction, which represents loss mechanisms in any reversible prelude to a thermal process. The example leads to a new type of availability. It is also the first example of a minimum time for transitions between thermal states of a thermodynamic system.

Shortcuts to adiabaticity: Fast-forward approach

“…Among other approaches let us mention (i) a transitionless tracking algorithm or "counterdiabatic" approach that adds to the original Hamiltonian extra terms to cancel transitions in the adiabatic or superadiabatic bases [8][9][10][11][12][13]; (ii) inverse engineering of the external driving [3,4,6,[21][22][23][24][25][26] based on Lewis-Riesenfeldt invariants [27], which has been applied in several expansion experiments [25,26]; (iii) optimal control (OC) methods [5,7,14,16], sometimes combined with other methods to enhance their performance [4,5,7]; (iv) the fast-forward (FF) approach advocated by Masuda and Nakamura [19,28]; (v) parallel adiabatic passage [29][30][31][32].…”

Fast driving between arbitrary states of a quantum particle by trap deformation

“…[17]), time-dependent microwave dressing [18], or, for ions in multisegmented Paul traps, time-dependent voltages applied to the control electrodes [19]. Such trap shaping on a short timescale has been proven useful, for example, to implement quantum thermodynamical cycles [20,21], or to implement a scalable architecture for quantum information processing [22]. It is also important for some quantum information processing schemes such as multiplexing and demultiplexing when information is encoded in external degrees of freedom [7], for Fock state creation [23], or velocity control [24,25], and it is expected to become more and more relevant given the current interest to develop quantum technologies.…”

Fast expansions and compressions of trapped-ion chains

“…Fast expansions/compressions without final excitation have been designed in a number of different ways [21][22][23][24][25][26][27]. Invariant-based engineering or scaling methods [24,25] were realized experimentally for a non-interacting coldatom cloud [28] and a Bose-Einstein condensate [28,29].…”