Gauging a Quantum Heat Bath with Dissipative Landau-Zener Transitions

Abstract

We calculate the exact Landau-Zener transitions probabilities for a qubit with arbitrary linear coupling to a bath at zero temperature. The final quantum state exhibits a peculiar entanglement between the qubit and the bath. In the special case of a diagonal coupling, the bath does not influence the transition probability, whatever the speed of the Landau-Zener sweep. It is proposed to use Landau-Zener transitions to determine both the reorganization energy and the integrated spectral density of the bath. Possible applications include circuit QED and molecular nanomagnets.PACS numbers: 32.80. Bx, 74.50.+r, 32.80.Qk, 03.67.Lx Quite a number of quantum two-state systems are presently tested as candidate qubits, the units of quantum information. Good qubits are well isolated from their environment, but easy to manipulate. This somewhat conflicting requirement has spurred renewed interest in the dynamics of qubits coupled to an environment or heat bath [1,2]. Qubits can be seen as bath detectors. For example, static qubits probe via their decay rates the bath spectral density at their transition frequencies. In solid-state environments these rates can be strongly frequency-and sample-dependent. We discuss an in this respect superior 'bath detection mode' of the qubit.One way of changing the state of a two-level system involves the forced crossing of its diabatic energies. For constant level-crossing speed this is known as the Landau-Zener (LZ) problem [3,4,5], which for a twolevel system can be solved exactly [3,4,5,6]. This is no longer the case when taking its environment into account [7,8,9, 10] that may cause thermal excitation and quantum tunneling. In the low-temperature tunneling regime, analytical estimates for transition probabilities exist only for very fast and very slow sweeps, and the literature is not unanimous about the latter limit [7,8,9,10,11].In another line of research, incited by the paper [12], it was recently proven that LZ transition probabilities can be calculated exactly for some many-level systems as well, although only for some initial states [13,14,15,16]. In this Letter, we extend the analysis to quantum dissipative systems and study LZ transitions in spin-boson problems in a new way. First we calculate zero-temperature LZ transition probabilities exactly. Second, by making use of this exact dependence on the bath parameters, we propose to gauge the dissipative environment of a qubit by performing LZ sweeps. One advantage of this bath detection mode of the qubit is that effects of spiky bath spectral densities are averaged out in every sweep.Driven spin-boson model.-Consider LZ transitions in a qubit coupled to a bath of N quantum harmonic oscillators, as described by the Hamiltonianwith the qubit-oscillator coupling. (2) The energy difference between the diabatic qubit states changes linearly in time as vt (with level-crossing speed v > 0) and their intrinsic interaction amplitude is ∆. The σ x,z are Pauli operators. The first two terms of (1) define the standard Landau-Zener proble...

Dissipative Landau-Zener problem and thermally assisted Quantum Annealing

“…In presence of a transverse coupling, the situation changes drastically: an exact analysis 23,24 at T = 0 shows that P gs (v, T = 0) can be enhanced with respect to the coherent probability P LZ gs (v). On the contrary, the finite-T behaviour of P gs (v, T ), and the possibility of a "thermally assisted" QA, i.e., a beneficial effect due to the bath, has not been properly scrutinized.…”

“…Couplings of this kind have already been considered in the literature, precisely in the present dissipative LZ context [23][24][25][26][27] . A number of results are known on this problem, both exact 23,24 at zero temperature and numerical at finite temperature [25][26][27] , obtained by means of a perturbative quantum master equation (QME) approach and by the so-called quasi-adiabatic path integral (QUAPI) 28,29 . Let P gs (v, T ) denote the probability that the system remains in the ground state ofĤ Q (t) when evolving from the ground state at t = −∞ up to t = +∞ in presence of a thermal bath at temperature T .…”

Thermally assisted quantum annealing of a 16-qubit problem

“…An open system with T ¼ 0 has been theoretically predicted to behave similarly to a closed system for such an anticrossing 10,[34][35][36] . In this experiment, it was infeasible to reduce T below B20 mK.…”

Monitoring entanglement evolution and collective quantum dynamics

“…In this context, one needs to take care of the interplay of decoherence and the external sweep velocity and its impact on the LZ probability and dynamics. 29,34,35 Toward the end of the sweep, one notices a deviation between the predicted phase φ 0 hf (t) and φ exp out (t), which becomes curved upward. This stems from the presence of higher charge states, which get slightly populated as soon as N g reaches the next half-integer value N deg g + 1, that is, the subsequent level anticrossing in the CPB spectrum.…”

“…(40)], but rather has to be computed from the definition of the two-qubit concurrence [Eq. (35)]. In order to test how much information about the concurrence C(t) is nevertheless contained in the measurement signal (43), we study the time evolution for the preparation in an unpolarized …”