Shortcuts to adiabaticity assisted by counterdiabatic Born–Oppenheimer dynamics

Abstract

Shortcuts to adiabaticity (STA) provide control protocols to guide the dynamics of a quantum system through an adiabatic reference trajectory in an arbitrary prescheduled time. Designing STA proves challenging in complex quantum systems when the dynamics of the degrees of freedom span different time scales. We introduce counterdiabatic Born-Oppenheimer dynamics (CBOD) as a framework to design STA in systems with a large separation of energy scales. CBOD exploits the Born-Oppenheimer approximation to separate the Hamiltonian into effective fast and slow degrees of freedom and calculate the corresponding counterdiabatic drivings for each sub-system. We show the validity of the CBOD technique via an example of coupled harmonic oscillators, which can be solved exactly for comparison, and further apply it to a system of two-charged particles.

Solution to the Time-Dependent Coupled Harmonic Oscillators Hamiltonian with Arbitrary Interactions

“…Time-dependent harmonic oscillators arise in quantum mechanical systems such as optical trapping of different objects like atoms and molecules [1,2], living cells, including viruses and bacteria [3,4]. Extensions to coupled time-dependent harmonic oscillators arise in several quantum mechanical problems, such as ion-laser interactions [1], quantized fields propagating through dielectric media [5], shortcuts to adiabaticity [6,7], the Casimir effect [8,9], as a toy model to study aspects of the final stages of black-hole evaporation [10], and their Schmidt modes in the study of quantum entanglement [11].…”

“…The simple extension to two coupled time-dependent harmonic oscillators has been considered and its solution presented by Macedo and Guedes for a very limited case of time-dependent functions [23]. Duncan and del Campo [7] solved the time-dependent coupled harmonic oscillator by considering the time-dependent coefficients as being, effectively, time independent. The Ermakov-Lewis invariant has also been proposed for systems of coupled harmonic oscillators [24].…”

“…Summarily, to the best of our knowledge, we present here for the first time, the solution to the problem of two coupled harmonic oscillators with completely arbitrary time-dependent parameters. Former solutions were given only for time-dependent parameters that were related among themselves [23] or were considered constant by using approximate adiabatic techniques [7].…”

Shortcuts to adiabaticity in Fermi gases

“…When this is not the case, alternative methods are desirable. Prominent examples, with complementary advantages and varying range of applicability, include the fast-forward technique [31,34,35], the use of invariant of motions and scaling laws [9,[36][37][38][39][40][41][42], classical flow fields [43], the existence of Lax pairs in integrable systems [44], and counterdiabatic Born-Oppenheimer dynamics [45].…”

Superadiabatic thermalization of a quantum oscillator by engineered dephasing

“…Hence, the possibility to speed up the dynamics of open quantum systems is highly desirable in view of applications to cooling, and more generally, in finite-time thermodynamics. In this context, the nonadiabatic control of composite and open quantum systems using STA remains an exciting open problem on which few results are available [34][35][36][37][38][39].…”