Interaction-induced quantum dephasing in mesoscopic rings

Golubev, Dmitri S.; Herrero, Carlos P.; Zaikin, Andrei D.

doi:10.1209/epl/i2003-00537-2

Cited by 26 publications

(83 citation statements)

References 25 publications

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“…However in recent works [16,17,18] the mass renormalization concept appears in a new context. The free energy F(T, Φ) of a particle in a ring is calculated, where T is the equilibrium temperature and Φ is the Aharonov Bohm flux the through the ring.…”

Section: Mass Renormalizationmentioning

confidence: 99%

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Dephasing of a particle in a dissipative environment

Cohen

Horovitz

2007

J. Phys. A: Math. Theor.

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Abstract. The motion of a particle in a ring of length L is influenced by a dirty metal environment whose fluctuations are characterized by a short correlation distance ℓ ≪ L. We analyze the induced decoherence process, and compare the results with those obtained in the opposing Caldeira-Leggett limit (ℓ ≫ L). A proper definition of the dephasing factor that does not depend on a vague semiclassical picture is employed. Some recent Monte-Carlo results about the effect of finite temperatures on "mass renormalization" in this system are illuminated.

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Section: Mass Renormalizationmentioning

confidence: 99%

“…Disregarding the m = 0 Fourier component the following approximation can be obtained [16,17] for M ≫ 1…”

Section: Appendix a Modeling Of A Fluctuating Environmentmentioning

confidence: 99%

Dephasing of a particle in a dissipative environment

Cohen

Horovitz

2007

J. Phys. A: Math. Theor.

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“…This problem has been extensively investigated by instanton methods 14,15,16,17 20 shows µ ′ ≈ 1.8. Furthermore, the MC data shows that at any finite temperature an exponential form appears, with a temperature independent length.…”

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confidence: 99%

“…At τ → τ ′ (or at high frequencies ω) one can expand the sin 2 (...) in (2) and then S int → n α n n 2 dω|ω||θ m (ω)| 2 , identifying a dissipative system. The Caldeira Legget bath has a single α n with α 1 = γR 2 while a charged particle in a dirty metal bath has 8,20 α n ≈ 2γ πr ln(r/n) for 1 < n r and α n ≈ 0 otherwise; here ℓ is the mean free path, k F is the Fermi wavevector, r = R/ℓ and γ = 3/(8k 2 F ℓ 2 ). As a new realization of Eq.…”

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confidence: 99%

Interference in the presence of dissipation

Horovitz

Doussal

2006

Phys. Rev. B

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We study a particle on a ring in presence of various dissipative environments. We develop and solve a variational scheme assuming low frequency dominance. We analyze our solution within a renormalization group (RG) scheme to all orders which reproduces a 2 loop RG for the CaldeiraLegget environment. In the latter case the Aharonov-Bohm (AB) oscillation amplitude is exponential in −R 2 where R is the ring's radius. For either a charge or an electric dipole coupled to a dirty metal we find that the metal induces dissipation, however the AB amplitude is ∼ R −2 for large R, as for free particles. Cold atoms with a large electric dipole may show a crossover between these two behaviors.PACS numbers: 73.23. Ra, The problem of interference and dephasing in presence of dissipative environments is of significance for a variety of experimental systems and a fundamental theoretical issue. The experimental systems include mesoscopic rings embedded on various surfaces where Aharonov-Bohm (AB) oscillations can be measured 1,2 , and the related problem of decoherence at low temperatures 3 . A different type of experimental systems are cold atom traps created by atom chips 4,5,6 , or trapped excited atoms with huge electric dipoles 7 . The atom chip that produces a magnetic or electric trap for the cold atoms necessarily also produces noise. Our problem is then relevant for evaluating the interference amplitude of cold atoms or molecules in presence of such noise.As an efficient tool for monitoring the effect of the environment we follow a suggestion by Guinea 8 to find the AB oscillation amplitude as function of the radius R of the ring, as measured by the curvature 9,10 1/B c of the ground state energy E 0 at external flux φ x = 0, i.e. 1/B c = ∂ 2 E 0 /∂φ 2 x | 0 . For free particles of mass M this amplitude is the mean level spacing ∼ 1/M R 2 . Two types of environments were suggested to lead to an anomalous suppression, i.e. a stronger decrease of the oscillation amplitude than 1/R 2 : system (i) is that of a Caledeira Legget bath and system (ii) of a charge in a dirty metal environment.System (i) is relevant to the Coulomb blockade problem 9,10,11,12 as well as to quantum dots at a distance from metallic gates 13 . This problem has been extensively investigated by instanton methods 14,15,16,17 , by RG methods 8,9,18 , and by Monte Carlo (MC) methods 9,10,19 . All methods show that B c increases exponentially with the dissipation strength α, i.e. B c ∼ α −µ e π 2 α , with differences in the exponent µ. In 2nd order renormalization group 9 (RG) µ = 2 , real time RG gives 18 µ = 6.5, instanton methods give either 14 µ = 2 or 15,17 µ = 3, or 16 µ = 4, while MC suggests 19 µ = 5. This system was also studied by a variational approach 21 which was solved numerically showing a nonperturbative regime at strong α. Since α = γR 2 where γ is a friction coefficient, a length scale π/ √ γ is identified 8 , beyond which the AB oscillations decay.The system (ii) was investigated by RG methods 8 finding B c ∼ R 2+µ ′ with µ ′ 1 nonunivers...

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“…[20] provides a discussion based on a quantum Langevin approach. Closely related works investigate the effect of a fluctuating Aharonov-Bohm flux [21], the effect of charge fluctuations in nearby pure and disordered conductors [22,23] and the effect of hot bosonic baths [24].…”

Section: The Mesoscopic Persistent Current Qubitmentioning

confidence: 99%

Ground state entanglement energetics

Büttiker

Jordan

2005

Physica E: Low-dimensional Systems and Nanostructures

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We consider the ground state of simple quantum systems coupled to an environment. In general the system is entangled with its environment. As a consequence, even at zero temperature, the energy of the system is not sharp: a projective measurement can find the system in an excited state. We show that energy fluctuation measurements at zero temperature provide entanglement information. For two-state systems which exhibit a persistent current in the ground state, energy fluctuations and persistent current fluctuations are closely related. The harmonic oscillator serves to illustrate energy fluctuations in a system with an infinite number of states. In addition to the energy distribution we discuss the energy-energy time-correlation function in the zero-temperature limit.

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Interaction-induced quantum dephasing in mesoscopic rings

Cited by 26 publications

References 25 publications

Dephasing of a particle in a dissipative environment

Dephasing of a particle in a dissipative environment

Interference in the presence of dissipation

Ground state entanglement energetics

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