Temperature can enhance coherent oscillations at ... - Robert S Whitney

Spin-interaction + symmetry of cluster. =⇒ ground-state = LARGE S. Spin-states relax at temperatures > few Kelvin. Two possible scenarios for this;. (a) nuclear ...
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Laboratoire de Physique et Modelisation ´ des Milieux Condenses ´ Univ. J. Fourier & CNRS, Grenoble, France

Temperature can enhance coherent oscillations at a Landau-Zener transition Robert S. Whitney1,2 , Maxim Clusel2,3 , Timothy Ziman1,2 1. LPMMC, Univ. J. Fourier & CNRS, Grenoble 2. Institut Laue Langevin, Grenoble 3. Laboratoire des Collo¨ıdes, Verres et Nanomat´ eriaux, Univ. Montpellier II & CNRS

Phys. Rev. Lett. 107, 210402 (2011) GDR Physique Quantique Mesoscopique, ´ Decembre ´ 2011

[1] SUMMARY Typically: coupling to environment causes decoherence

...BUT we show that an environment can also enhance coherent oscillations. ⇒ coherent osc. grow strongly with increasing temperature

Origin in Lamb-shift ⇒ we call effect

\Lamb-assisted oherent os illations"

♣ New probe for high-frequency environments in

qubits, mole ular magnets, et .

[2] MODEL instantaneous eigenenergies

SYSTEM

e.g. bath of bosons temperature = T



time, t

adia

bati

System Hamiltonian:

LARGE ENVIRONMENT

c

Landau-Zener

OR CLASSICAL NOISE

HtLZ = − 21 νt σz + ∆ σx



Full Hamiltonian — system+environ. Htsys&env = HtLZ − 12 σz X + Henv with X operator acting weakly on a huge number of environ. modes, Henv .

[3] RESULTS (b) Lamb shift and no decoherence

(a) Decoherence and no Lamb-shift =⇒ suppresses oscillations

High-freq. environment

Markovian environ. (white-noise) sx (t )

=⇒ ENHANCES oscillations

1

sx (t )

dashed: no coupling to env. solid: coupled to env.

1

dashed: no coupling to env. solid: coupled to env. 1 2

1 2

ν 1/2 t -8

-4

4

sy (t ) - 12

sz (t ) -1

8

A

12

11111111111111111111 00000000000000000000 00000000000000000000 11111111111111111111 A vs. ξzR 00000000000000000000 11111111111111111111 æ 00000000000000000000 11111111111111111111 æ æ 00000000000000000000 11111111111111111111 0.1 ∆/ν 1/2= 2.0 æ 00000000000000000000 11111111111111111111 æ à æ 00000000000000000000 11111111111111111111 à æ 00000000000000000000 11111111111111111111 à à 00000000000000000000 11111111111111111111 à 00000000000000000000 11111111111111111111 à 2.4 0.01ì à 00000000000000000000 11111111111111111111 ì 00000000000000000000 11111111111111111111 ì ì 00000000000000000000 11111111111111111111 ì 00000000000000000000 11111111111111111111 ì 2.8 ì 00000000000000000000 11111111111111111111 ò ò 0.001 00000000000000000000 11111111111111111111 ò 00000000000000000000 11111111111111111111 ò 00000000000000000000 11111111111111111111 ò ò 3.2ò 00000000000000000000 11111111111111111111 00000000000000000000 11111111111111111111 00000000000000000000 11111111111111111111 00000000000000000000 11111111111111111111 0.05 0.1 0.15 00000000000000000000 11111111111111111111 00000000000000000000 11111111111111111111 00000000000000000000 11111111111111111111

ν 1/2 t -8

-4

sy (t )

sz (t )

4

8

12

A 000000000000000000000 111111111111111111111 A vs. γ 000000000000000000000 111111111111111111111 0.5 ∆/ν 1/2æ= 2.0 æ 111111111111111111111 æ - 12 000000000000000000000 æ 000000000000000000000 111111111111111111111 æ æ æ 000000000000000000000 111111111111111111111 2.4à 000000000000000000000 111111111111111111111 à à 0.1 000000000000000000000 111111111111111111111 à à 000000000000000000000 111111111111111111111 à 2.8ì à 000000000000000000000 111111111111111111111 ì 000000000000000000000 111111111111111111111 ì 000000000000000000000 111111111111111111111 ì ì 000000000000000000000 111111111111111111111 3.2ò ì -1 111111111111111111111 000000000000000000000 0.01ì ò 000000000000000000000 111111111111111111111 ò 000000000000000000000 111111111111111111111 ò 000000000000000000000 111111111111111111111 ò 000000000000000000000 111111111111111111111 ò 000000000000000000000 111111111111111111111 ò 000000000000000000000 111111111111111111111 0.001 000000000000000000000 111111111111111111111 000000000000000000000 111111111111111111111 000000000000000000000 111111111111111111111 0.1 0.2 0.3 000000000000000000000 111111111111111111111 000000000000000000000 111111111111111111111 000000000000000000000 111111111111111111111

[4] From LAMB-SHIFT to TEMPERATURE-DEPENDENCE “Lamb-shift = level-repulsion” Competition between: (1) Lamb-shift ⇐ high-freq. modes reduces system gap while low-freq. modes increase gap

(2) decoherence ⇐ env. modes in resonance with system gap

⇒ Multiple regimes with with

K T

strongly (ε>1) super−Ohmic

with with

K T

with with

K T

with with

K T

weakly (0