Shortcuts to adiabaticity in the presence of a continuum: Applications to itinerant quantum state transfer

Abstract

We present a method for accelerating adiabatic protocols for systems involving a coupling to a continuum, one that cancels both non-adiabatic errors as well as errors due to dissipation. We focus on applications to a generic quantum state transfer problem, where the goal is to transfer a state between a single level or mode, and a propagating temporal mode in a waveguide or transmission line. Our approach enables perfect adiabatic transfer protocols in this setup, despite a finite protocol speed and a finite waveguide coupling. Our approach even works in highly constrained settings, where there is only a single time-dependent control field available.Introduction-Adiabatic quantum evolution provides an efficient and robust way to implement a variety of important quantum operations including state transfer [1][2][3][4][5][6][7], state preparation [8][9][10][11], and even quantum logic gates [12][13][14]. While such protocols are robust against timing errors, they are necessarily slow, making them vulnerable to dissipation or fluctuations. There is thus considerable interest in finding ways to accelerate adiabatic protocols, such that fast evolution is possible without significant non-adiabatic errors [15][16][17][18][19]. These techniques are generally referred to as "shortcuts to adiabaticity" (STA), and involve modifying control fields to suppress the net effect of non-adiabatic errors [20][21][22][23][24][25]. Recent experiments have successfully implemented versions of these strategies [26][27][28][29][30].A key drawback of the transitionless driving strategy and its higher order variants [20][21][22][23][24][25] is that they require the exact diagonalization of a time-dependent Hamiltonian, making them unwieldy for systems with many degrees of freedom. They are thus unsuitable for an important class of quantum state transfer problems, where the goal is to transfer an initial state in a localized system having discrete energy levels to a propagating state in a continuum such as a waveguide or a transmission line (see, e.g., [31][32][33]).In this paper we present a general method for applying STA to the above class of problems. The method is based on first deriving an effective non-Hermitian Hamiltonian, and then constructing dressed-states and modified control sequences that suppress both non-adiabatic errors (due to finite protocol speed) and "dissipative" errors (due to the coupling to the continuum). We apply our technique to two ubiquitous quantum state transfer problems based on STIRAP (stimulated Raman adiabatic passage) [2]. Such protocols have been discussed in systems ranging from atomic cavity QED setups [31,32] to optomechanics [34]. Remarkably, we show that our method works even in the highly constrained protocol introduced by Duan et al. [32], where there is only a single time-dependent control field in the Hamiltonian.Our work represents a substantial advance over previous work using STA to accelerate adiabatic state transfer [20][21][22][23][24][25], as these works did not include a coupling to ...

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