Ehrenfest dynamics and frictionless cooling methods

Abstract

Recently introduced methods which result in shortcuts to adiabaticity, particularly in the context of frictionless cooling, are rederived and discussed in the framework of an approach based on Ehrenfest dynamics. This construction provides physical insights into the emergence of the Ermakov equation, the choice of its boundary conditions, and the use of minimum uncertainty states as indicators of the efficiency of the procedure. Additionally, it facilitates the extension of frictionless cooling to more general situations of physical relevance, such as optical dipole trapping schemes. In this context, we discuss frictionless cooling in the short-time limit, a complementary case to the one considered in the literature, making explicit the limitations intrinsic to the technique when the full three-dimensional case is analyzed.

Classical and Quantum Shortcuts to Adiabaticity for Scale-Invariant Driving

“…Similarly, optimal trajectories for efficient transport [77] can be adopted for scale-invariant driving with f (t) = 0. Furthermore, an analysis of the Ehrenfest dynamics [79] in CD protocols can be used as a guideline to engineer modulations of both γ(t) Shortcut to an adiabatic expansion by local counterdiabatic driving. Whenever the trapping potential U(q, t) = U0(q/γ(t))/γ(t) 2 (with f (t) = 0), the auxiliary counterdiabatic term modulated by −mγ/γ(t) induces a non-adiabatic self-similar dynamics which reduces to the target state Ψ(t) at t = {0, τF}, when the auxiliary term vanishes.…”

Scaling-Up Quantum Heat Engines Efficiently via Shortcuts to Adiabaticity

“…This is achieved by tailoring excitations during the nonequilibrium process. STA applicable to the expansion and compression strokes often used in thermodynamic cycles has been extensively studied in recent years, both theoretically [23][24][25][26][27][28][29][30][31][32][33][34][35] and experimentally with ultracold atomic gases [36,37]. The development of STA applicable to many-body systems has been reported in [29,31,[38][39][40][41][42][43] and further demonstrated in the laboratory [44].…”

Shortcuts to adiabaticity assisted by counterdiabatic Born–Oppenheimer dynamics

“…The first term in (19) is recognized as the spectral decomposition of the original system Hamiltonianˆ( ) H t 0 . The second term,Ĥ 1 , is the auxiliary CD term required so that the adiabatic trajectory y ñ | ( ) t n ad in equation (15) becomes an exact solution of (16), that is the Schrödinger equation for the full driving Hamiltonian = +ˆĤ H H 0 1 . When the energy spectrum ofĤ 0 is non-degenerate, the additional CD term can be recasted using the differential of the time-independent Schrödinger equation of the original system Hamiltonian [4]…”

“…They can be used to guide the dynamics of systems with a discrete energy spectrum [2][3][4][5][6][7], as shown in the laboratory [8][9][10][11]. Similarly, STA can be used to control the degrees of freedom of continuous variables systems [1,[12][13][14][15][16][17][18][19] as demonstrated by the fast control of a trapped ion in phase space [20]. In the context of trapped ultracold atoms, early theoretical results indicated that STA could be applied to many-body systems [17,[21][22][23].…”