Transmission of a single electron through a Berry's ring

A theoretical model of transmission and reflection of an electron with spin is proposed for a mesoscopic ring with rotating localized magnetic moment. This model may be realized in a pair of domain walls connecting two ferromagnetic domains with opposite magnetization. If the localized magnetic moment and the traveling spin is ferromagnetically coupled and if the localized moment rotates with opposite chirality in the double-path, our system is formulated in the model of an emergent spin-orbit interaction in a ring. The scattering problem for the transmission spectrum of the traveling spin is solved both in a single path and a double path model. In the double path, the quantum-path interference changes dramatically the transmission spectrum due to the effect of the Berry's phase. Specifically, the spin-flip transmission and reflection are both strictly forbidden

Coherent destruction of tunneling, dynamic localization and the Landau-Zener formula

We clarify the internal relationship between the coherent destruction of tunneling (CDT) for a two-state model and the dynamic localization (DL) for a one-dimensional tight-binding model, under the periodical driving field. The time-evolution of the tight-binding model is reproduced from that of the two-state model by a mapping of equation of motion onto a set of ${\rm SU}(2)$ operators. It is shown that DL is effectively an infinitely large dimensional representation of the CDT in the ${\rm SU}(2)$ operators. We also show that both of the CDT and the DL can be interpreted as a result of destructive interference in repeated Landau-Zener level-crossings.Comment: 5 pages, no figur

Gauging a quantum heat bath with dissipative Landau-Zener transitions

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.Comment: 4 pages, 1 figur

Gauging a quantum heat bath with dissipative Landau-Zener transitions,

I. Abstract We calculate the exact Landau-Zener (LZ) transition probabilities for a qubit with arbitrary linear coupling to a bath at T = 0 (K). The bath causes time-dependent relaxation of the qubit; dephasing has little or no influence. Applications include circuit QED II. Introduction: Landau-Zener transitions Exactly solvable dynamics Expect effects of bath-induced dephasing ∝ cos θ and relaxation ∝ sin θ. III. Method and "No-go-up theorem" [1,3] Method: Qubit-bath entanglement [1]: Final state |ψ(∞)〉 = P ↑→↑ |↑, 0 ↑ 〉 + 1 − P ↑→↑ n c n |↓, n ↓ 〉. IV. Transverse coupling (θ = π/2) ⇒ Relaxation [2] Spectral density As for an isolated qubit! VI. Gauging a quantum heat bath [3] Central result: Exact transition probability for arbitrary bath coupling: which involves the reorganization energy E 0 = ħ 4π ∞ 0 dω J (ω)/ω. Gauging: measure E 0 and S ⇒ fix parameters of spectral densities J (ω). Idea: vary ∆ to find ∆ min for which P ↑→↓ (∞) is minimal. ∆ min gives E 0 and P min ↑→↓ (∞) gives S. For J (ω) = αωe −ω/ωc , ħω c = S/(E 0 )

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

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 off-diagonal 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.Comment: 16 pages, 8 figure