Quantum Nucleation of Charge & Flux Solitons

John H. Miller, Jr. A. I. Wijesinghe, Z. Tang, & A. M. Guloy

Dept. of Physics, Dept. of Chemistry, &Texas Center for Superconductivity

University of Houston

jhmiller@uh.edu

ECRYS - 2011August 16, 2011

Tunneling of BEC Solitons (Hulet group)

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Bright matter wave solitons

105 7Li atoms x 13,000me

M > 109 me

Macroscopic wavefunctions tunnel through opticalbarrier (w/ transmitted & reflected components).

Tunneling probability:

Agrees w/ experiment only if m & V taken to be single atom quantities.

Hybrid between Josephson tunneling & MQT. BEC soliton = quantum fluid.

Quantum fluid: Each particle delocalized over l > interparticle spacing.CDW = quantum fluid: Each e- delocalized over long distances.

CDW dielectric response: Classical predictions vs. experiment

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1. Random pinning model: Littlewood PR B 33 6694 (1986). 2. CF: Coppersmith & Fisher PR A 38 6338 (1988). 3. NM: Narayan & Middleton PR B 49, 244 (1994).4. ZG: Zettl & Grüner PR B 29 755 (1984);

WMG: Wu, Mihaly, & Grüner Solid State Commun. 55 663 (1985).

Other ac responses flat below threshold.

JHM et al. PR B 31 5229 (1985).

Nucleation of Charge of Flux Soliton Pairs

Q0 = 2Nerc, internal field

JHM, Ordóñez, Prodan PRL 84 1555 (2000);

JHM et al. J. Phys. A 36 9209 (2003); S. Coleman, Ann. Phys. 101, 239 (1976).

Magnetic blockade effect for Josephson vortex pair nucleation:

= Coulomb blockade threshold.

ET Coulomb Blockade << ET Classical

Energy difference:

Widom & Srivastava, Phys. Lett. 114A, 337 (1986).

ET (Coulomb blockade) increases w/ nimpurity

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Coulomb blockade threshold field: ET = Q0/2e A = eNrc /e A Grüner empirical relation emerges naturally!

e ET = ercnch (nch = N/A, rc = condensate fraction)

G. Grüner, Rev. Mod. Phys. 60, 1129 (1988).

Derived relation for classical depinning field Ecl (Grüner):

e Ecl = 4percnch

ET (Coulomb blockade) = Ecl /4p

Expect ET (C.B.) ni

2 for weak pinning.

Time Correlated Soliton Tunneling

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‘Vacuum angle’:

Pinning & electrostatic energy (per chain):

JHM, Ordóñez & Prodan PRL 84 1555 (2000).JHM, Cárdenas, et al. J. Phys. A 36 9209 (2003); S. Coleman, Ann. Phys. 101, 239

(1976).

Charging energy:

Tunneling (‘false vacuum’ decay) when q > p (or q – 2pn > p).

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Explains flat dielectric response

uE/up = 1

uE/up = 0.6

uE/up = 0.2

uE/up = 0.015

JHM, Ordóñez, & Prodan PRL 84 1555 (2000).

Ross, Wang, & Slichter PRL 56 663 (1986).

t = uE/up

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h/2e oscillations in CDW magnetoconductance

Latyshev et al, PRL 78, 919 (1997).

NbSe3 with columnar defects h/2e quantum interference in CDW rings.

Tsubota et al, Physica B 404 416–418 (2009).(Tanda group, Hokkaido U., Sapporo, Japan)

Contrasts w/ h/2Ne prediction (e.g. Bogachek et al, PRB 42, 7614 (1990)).

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Proposed model to simulate DW dynamics

Analogous to time-correlated single-electron tunneling (Averin & Likharev, J. Low T. Phys. 62 345 (1986))

Defining: & yields:

Use of probability amplitudes, TDSE

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Motivated by Feynman Lectures, vol. III treatment of Josephson junction.

Introduce field-dependent tunneling Hamiltonian matrix element:

Amplitude for density wave to be on branch n:

Time-dependent Schrödinger equation = “classical” Eq. of motion.

[idn]

Probability amplitudes, TDSE: Results

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Probability amplitudes, TDSE: Results (continued)

12Solid lines – theory; Dashed Lines - experiment

Experimental data –McCarten group, PRB2000.

9.90 mA

10.89 mA

11.49 mA

11.88 mA

Probability amplitudes, TDSE: Results (continued)

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Dotted lines:

Jcdw ~ [E ETm]exp[E0/E]

Thorne, Miller, et al, PRL 55, 1006 (1985)

TDSE: Theory vs. Experiment on dV/dI

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NbSe3

Phase Diagram – Soliton Nucleation vs. Classical Depinning

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Blue bronze data (Mihaly et al)

h/2e Aharonov-Bohm oscillations in CDW rings

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Time-varying vector potential Modulates phase of wavefunction

TaS3 – 185 K

JHM ... Bardeen, PRL 51, 1592 (1983); PRB 31, 5229 (1985); JHM, PhD dissertation (1985).

Nonlinear mixing vs. Photon assisted tunneling theory

“Bells & whistles:” Model with multiple domains

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Inclusion of nonlinear terms:

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g’ = .001 g’ = .01 g’ = .02

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Alternative approach: Use of Probabilities

Let p = probability f tunnels from branch n to n+1.

Then:

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Fixed time interval (non-integer # of cycles) used when averaging voltage

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Theory Experiment (Cornell group)

Thickness dependence of Ic in YBCO coated conductors

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Pair creation current, d > l: Effective 2D penetration length:

V - I curve of YBCO grain boundary junction

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Data from R. D. Redwing et al., APL 75, 3171 (1999).

Classical RSJ model:

Quantum Simulations(solid lines)

86 K

82.5K

77.2K

75K

70K

Superconducting iron pnictide bi-crystal junction

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Data from X. Zhang et al., APL 95, 062510 (2009).

4.2 K

Broader implications of model

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Spontaneous CP violation: “q = p” instability e.g. D. Boer, J. K. Boomsma, PRD 78, 054027 (2008). Michel H. G. Tytgat, PRD 61, 114009 (2000).

q = p instabilities have also been proposed for: - Quantum Hall effect - Topological Insulators

Quantum cosmology:

Quantum creation of universe(s) Phase transitions in the early universeTunneling of universe small ( 0) cosmological constant

e.g. P. J. Steinhardt, N. Turok, Science 312, 1180 (2006).

Concluding Remarks

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Quantum theory is the most ubiquitous, universally applicable theory known to man.

The laws of quantum physics govern every system of particles in the universe, & probably the universe as a whole.

One of those laws (Murray Gell-Mann’s totalitarian principle) is:

“Everything not forbidden is compulsory.”

Acknowledgements

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Previous collaborators: John Tucker, John Bardeen, UIUCDocumentary, book:http://1m1f.com/video/OyV8qSwGUHU/Spark-of-Genius-The-Story-of-John-Bardeen-at-the-University-of-Illinois.html

Articles about and by John Bardeen:David Pines, Physics Today, April 1992.Proc. Am. Phil. Soc. 153, 287 (2009).John Bardeen, Physics Today, December 1990.

Previous collaborators (continued):Emil Prodan (currently at Yeshiva U.), Carlos Ordonez (UH), John McCarten, Amitesh Maiti

Current collaborators (UH): Asanga I. Wijesinghe, Zhongjia Tang, Arnold M. Guloy

Funding: NIH, Texas: Texas Ctr. for Superconductivity

August 16, 2011 28ECRYS 2011jhmiller@uh.edu

Thank you!