Dissipative Landau-Zener transitions of a qubit: Bath-specific and universal behavior

Abstract

We study Landau-Zener transitions in a qubit coupled to a bath at zero temperature. A general formula is derived that is applicable to models with a non-degenerate ground state. We calculate exact transition probabilities for a qubit coupled to either a bosonic or a spin bath. The nature of the baths and the qubit-bath coupling is reflected in the transition probabilities. For diagonal coupling, when the bath causes energy fluctuations of the diabatic qubit states but no transitions between them, the transition probability coincides with the standard LZ probability of an isolated qubit. This result is universal as it does not depend on the specific type of bath. For pure offdiagonal coupling, by contrast, the tunneling probability is sensitive to the coupling strength. We discuss the relevance of our results for experiments on molecular nanomagnets, in circuit QED, and for the fast-pulse readout of superconducting phase qubits.

Dissipative Landau-Zener problem and thermally assisted Quantum Annealing

“…It is known that aσ z -coupling alone cannot be truly beneficial to P gs (v, T ). This has been established both exactly, at zero temperature -where the actual P gs (v, T = 0) is completely unaffected by the bath 24 and coincides with the well-known Landau-Zener 30,31 coherent evolution result P LZ gs (v) = 1 − e −π∆ 2 /(2 v) -, and numerically at finite temperature 25,27 .…”

“…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 .…”

“…II for precise definitions). The black solid line is the coherent-evolution result P LZ gs (v), the black dashed line in panel (b) is the probability Pgs(v, T = 0) obtained by means of the exact analytical result at zero temperature 24 , while the various points are QME data for different bath temperatures. Black arrows indicate the direction of increasing T .…”

Entanglement and disentanglement in circuit QED architectures

“…However, due to the symmetry of the Hamiltonian (1), every creation or annihilation of a photon is accompanied by a qubit flip, which restricts the resulting dynamics to the states |↑, 2n and |↓, 2n + 1 . Furthermore, the "no-go-up" theorem states that P ↑,n→↑,m = 0 for m>n [20]. This reduces 2 the possible final qubit-oscillator states to the state…”