Temperature can enhance coherent oscillations at ... - Robert S Whitney
Spin-interaction + symmetry of cluster. =â ground-state = LARGE S. Spin-states relax at temperatures > few Kelvin. Two possible scenarios for this;. (a) nuclear ...
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
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