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 - 2011
August 16, 2011
Tunneling of BEC Solitons (Hulet group)
Bright matter wave solitons
105 7Li atoms x 13,000me
 M > 109 me
Macroscopic wavefunctions
tunnel through optical
barrier (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.
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CDW dielectric response:
Classical predictions vs. experiment
JHM et al. PR B 31
5229 (1985).
Other ac responses flat
below threshold.
1.
2.
3.
4.
Random pinning model: Littlewood PR B 33 6694 (1986).
CF: Coppersmith & Fisher PR A 38 6338 (1988).
NM: Narayan & Middleton PR B 49, 244 (1994).
ZG: Zettl & Grüner PR B 29 755 (1984);
WMG: Wu, Mihaly, & Grüner Solid State Commun. 55 663 (1985).
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Nucleation of Charge of Flux Soliton Pairs
Q0 = 2Nerc,  internal field
Energy difference:
= Coulomb blockade threshold.
ET Coulomb Blockade << ET Classical
Magnetic blockade effect for Josephson vortex
pair nucleation:
JHM, Ordóñez, Prodan PRL 84 1555 (2000);
JHM et al. J. Phys. A 36 9209 (2003); S. Coleman, Ann. Phys. 101, 239 (1976).
Widom & Srivastava, Phys.
Lett. 114A, 337 (1986).
ET (Coulomb blockade) increases w/ nimpurity
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.
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Time Correlated Soliton Tunneling
‘Vacuum angle’:
 Pinning & electrostatic energy (per chain):
Tunneling (‘false vacuum’ decay) when q > p (or q – 2pn > p).
Charging energy:
JHM, Ordóñez & Prodan PRL 84 1555 (2000).
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JHM, Cárdenas, et al. J. Phys. A 36 9209 (2003); S. Coleman, Ann. Phys. 101, 239 (1976).
Explains flat dielectric response
uE/up = 1
uE/up = 0.6
t = uE/up
uE/up = 0.2
uE/up = 0.015
JHM, Ordóñez, & Prodan PRL 84 1555 (2000).
Ross, Wang, & Slichter PRL 56 663 (1986).
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h/2e oscillations in CDW magnetoconductance
NbSe3 with columnar defects
Latyshev et al, PRL 78, 919 (1997).
h/2e quantum interference in CDW rings.
Tsubota et al, Physica B 404 416–418 (2009).
(Tanda group, Hokkaido U., Sapporo, Japan)
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Contrasts w/ h/2Ne prediction (e.g. Bogachek et al, PRB 42, 7614 (1990)).
Proposed model to simulate DW dynamics
Defining:
&
yields:
Analogous to time-correlated single-electron tunneling
(Averin & Likharev, J. Low T. Phys. 62 345 (1986))
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Use of probability amplitudes, TDSE
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:
[idn]
Time-dependent Schrödinger equation = “classical” Eq. of motion.
10
Probability amplitudes, TDSE: Results
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Probability amplitudes, TDSE: Results (continued)
11.88 mA
11.49 mA
10.89 mA
9.90 mA
Experimental data –
McCarten group, PRB
2000.
Solid lines – theory; Dashed Lines - experiment
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Probability amplitudes, TDSE: Results (continued)
Dotted lines:
Jcdw ~ [E  ETm]exp[E0/E]
Thorne, Miller, et al, PRL 55, 1006 (1985)
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TDSE: Theory vs. Experiment on dV/dI
NbSe3
14
Phase Diagram –
Soliton Nucleation vs. Classical Depinning
Blue bronze data (Mihaly et al)
15
h/2e Aharonov-Bohm oscillations in CDW rings
16
Time-varying vector potential  Modulates phase of wavefunction
Nonlinear mixing vs.
Photon assisted tunneling theory
TaS3 – 185 K
JHM ... Bardeen, PRL 51, 1592 (1983);
PRB 31, 5229 (1985);
JHM, PhD dissertation (1985).
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“Bells & whistles:” Model with multiple domains
18
Inclusion of nonlinear terms:
g’ = .001
g’ = .01
g’ = .02
19
Alternative approach: Use of Probabilities
Let p = probability f tunnels from branch n to n+1.
Then:
20
Fixed time interval (non-integer # of cycles) used when
averaging voltage
Theory
Experiment (Cornell group)
21
Thickness dependence of Ic in YBCO coated conductors
Pair creation current, d > l:
Effective 2D penetration length:

22
V - I curve of YBCO grain boundary junction
Classical RSJ model:
82.5K
77.2K
86 K
75K
70K
Quantum
Simulations
(solid lines)
Data from R. D. Redwing et al., APL 75, 3171 (1999).
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Superconducting iron pnictide bi-crystal junction
4.2 K
Data from X. Zhang et al., APL 95, 062510 (2009).
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Broader implications of model
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 universe
Tunneling of universe  small ( 0) cosmological constant
e.g. P. J. Steinhardt, N. Turok, Science 312, 1180 (2006).
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Concluding Remarks
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.”
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Acknowledgements
Previous collaborators: John Tucker, John Bardeen, UIUC
Documentary, book:
http://1m1f.com/video/OyV8qSwGUHU/Spark-of-Genius-The-Story-of-John-Bardeen-atthe-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
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Thank you!
August 16, 2011
ECRYS 2011
jhmiller@uh.edu
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