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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
ECRYS - 2011August 16, 2011
Tunneling of BEC Solitons (Hulet group)
2
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
3
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
5
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
6
‘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).
7
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
8
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)).
9
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
10
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
11
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)
13
Dotted lines:
Jcdw ~ [E ETm]exp[E0/E]
Thorne, Miller, et al, PRL 55, 1006 (1985)
TDSE: Theory vs. Experiment on dV/dI
14
NbSe3
Phase Diagram – Soliton Nucleation vs. Classical Depinning
15
Blue bronze data (Mihaly et al)
h/2e Aharonov-Bohm oscillations in CDW rings
16
17
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
18
Inclusion of nonlinear terms:
19
g’ = .001 g’ = .01 g’ = .02
20
Alternative approach: Use of Probabilities
Let p = probability f tunnels from branch n to n+1.
Then:
-
Fixed time interval (non-integer # of cycles) used when averaging voltage
21
Theory Experiment (Cornell group)
Thickness dependence of Ic in YBCO coated conductors
22
Pair creation current, d > l: Effective 2D penetration length:
V - I curve of YBCO grain boundary junction
23
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
24
Data from X. Zhang et al., APL 95, 062510 (2009).
4.2 K
Broader implications of model
25
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).
Concluding Remarks
26
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
27
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 [email protected]
Thank you!