Transcript Superfluidity with disorder in a thin film of quantum gas

Disordered superfluid thin films with cold
atoms
𝜇𝐿
𝜇𝑅
S. Krinner, D. Stadler, J. Meineke, J.-P. Brantut and T. Esslinger
Institute for Quantum Electronics, ETH Zürich
Motivation
Two – dimensional
superconducting thin films
Superconductor – Insulator
Quantum Phase Transition
Control Parameter:
• Disorder Strength
• Film Thickness
• Magnetic Field
Mechanism: Bosonic vs Fermionic
A. Goldman, N. Markovic; Physics Today 51, 11 (1998)
V. Ganthmaker, V. Dolgopolov, Physics-Uspekhi 53, 1 (2010)
Experimental Setup
Degenerate Fermi Gas
• Atom number: 105 6Li atoms
• Temperature: 0.2 TF
Experimental Setup
Degenerate Fermi Gas
• Atom number: 105 6Li atoms
• Temperature: 0.2 TF
• Tunable Interactions
Experimental Setup
Geometry: Mesoscopic two-dimensional channel connected to two reservoirs
𝜇𝐿
𝜇𝑅
J.-P. Brantut et al., Science 337, 1069 (2012)
Inducing a chemical potential bias
Symmetric position
Inducing a chemical potential bias
Symmetric position
Shift trap (slow)
Inducing a chemical potential bias
Symmetric position
Shift trap (slow)
Evaporative cooling
Inducing a chemical potential bias
Symmetric position
Shift trap (slow)
Evaporative cooling
Shift trap back (fast)
Projection of a disordered potential
𝜇𝐿
𝜇𝑅
Tuning parameter: Disorder strength
Length scales
𝜎
Disorder: Correlation length 𝜎
Length scales
𝜎
Disorder: Correlation length 𝜎
BEC: Molecule pair size d ≪ 𝜎
Length scales
𝜎
Disorder: Correlation length 𝜎
Unitary Fermi Gas: pair size d ~ 𝜎
BEC - Resistance of disordered thin film
S. Krinner et al., PRL 110, 100601 (2013)
BEC - Breakdown of superfluid flow
S. Krinner et al., PRL 110, 100601 (2013)
BEC - Breakdown of superfluid flow
𝜎 = 0.29 𝜇𝑚
𝜇 = 400 𝑛𝐾
𝑎 = 3500 𝑎0
S. Krinner et al., PRL 110, 100601 (2013)
BEC - Breakdown of superfluid flow
Classical Percolation
Threshold: 𝑉/𝜇 = 1.92
S. Krinner et al., PRL 110, 100601 (2013)
𝜎 = 0.29 𝜇𝑚
𝜇 = 400 𝑛𝐾
𝑎 = 3500 𝑎0
Transport properties – Unitary Fermi Gas
Transport properties – Unitary Fermi Gas
𝜎 = 0.72 𝜇𝑚
𝜇 = 550 𝑛𝐾
𝑎=∞
Transport properties – Unitary Fermi Gas
Percolation threshold
for pairs
𝜎 = 0.72 𝜇𝑚
𝜇 = 550 𝑛𝐾
𝑎=∞
Insitu observation of a disordered Fermi Gas
20μm
Increasing disorder strength
Insitu observation of a disordered Fermi Gas
V
H
V
H
V
Increasing disorder strength
H
Percolation analysis
Percolation analysis
Level 𝑛
Percolation analysis
Level 𝑛
Percolation analysis
Level 𝑛
Percolation analysis
Level 𝑛
Percolation analysis
Level 𝑛
Percolation analysis
Level 𝑛
Percolation analysis
Level 𝑛
𝑉/𝜇 = 1.4
Percolation analysis
Level 𝑛
𝑉/𝜇 = 1.4
𝑉/𝜇 = 0.2
Percolation analysis
Percolation analysis
Fragmented
Regime
Smooth
Regime
Pair percolation
threshold
Conclusion – Unitary Fermi Gas
Increasing
Disorder
(arXiv soon)
Outlook: Thermoelectricity
J.-P. Brantut et al., arXiv: 1306.5754
Lithium Team
J.-P. Brantut
S. Krinner
D. Stadler
J. Meineke
T. Esslinger
We acknowledge fruitful discussions with: J. Blatter, T.Bourdel, A. Georges, T.
Giamarchi, V. Josse, C. Kollath, P. Lugan, C. Mueller, L.Pollet, T. Roscilde, D. Shahar, V.
Shenoy, A. Zheludev and W. Zwerger.
Summary
1) Transport measurements:
Classical Percolation
Threshold: 𝑉/𝜇 = 1.92
S. Krinner et al., PRL 110, 100601 (2013)
2) Insitu study
Percolation threshold
for pairs
Length scales
𝜎
Disorder: Correlation length 𝜎 = 0.72 μ𝑚
Unitary Fermi Gas:
Pair size d ~ 𝑘𝑓 −1 ~ 𝜎
Coherence length ξ ~ 𝑘𝑓 −1 ~ 𝜎
Disorder-induced breakdown of superfluid flow
Classical Percolation
Threshold: 𝑉/𝜇 = 1.92
S. Krinner et al., arxiv:1211.7272 (2012), accepted in PRL
Length scales
Outlook
Strongly correlated transport through projected structures
Current flow
Exponential decay of atom number imbalance Δ𝑁 = 𝑁left − 𝑁right
C
𝜏 = 𝑅𝐶 = 170ms
0.1
R
0
0.4
0.8
time (s)
𝑑
1
Δ𝑁 =
Δ𝑁
𝑑𝑡
𝑅𝐶
Finite resistance although transport through channel is ballistic!?
Conduction as transmission
Conduction is transmission from one reservoir to another (Landauer)
𝜇𝐿
𝜇𝑅
Conduction as transmission
Conduction is transmission from one reservoir to another (Landauer)
𝜇𝐿
𝜇𝑅
Contact resistance: Reflection at the contacts
Conduction as transmission
Conduction is transmission from one reservoir to another (Landauer)
𝜇𝐿
𝜇𝑅
Contact resistance: Reflection at the contacts
Dissipation takes place deeply inside the reservoirs
J.-P. Brantut et al., Science 337, 1069 (2012)
Why do we not see Josephson oscillations?
Length scales :
Channel: ~ 30 µm
Coherence length: ~ 1µm
Time scales :
Transport time: ~20 ms
Chemical potential diff.: ~ 3 kHz
The current has no chance to reverse
Disorder-induced breakdown of superfluid flow
Disorder-induced breakdown of superfluid flow
Drift velocity
Density independent quantity: Drift velocity: vd= 𝐼/𝑛𝑙
Disorder-induced breakdown of superfluid flow
Classical percolation threshold
Classical Percolation
Threshold: 𝑉/𝜇 = 1.92
Disorder-induced breakdown of superfluid flow
𝑅𝐵𝐸𝐶 𝜏𝑊𝐼𝐹 𝐶𝐵𝐸𝐶
=
𝑅𝑊𝐼𝐹 𝜏𝐵𝐸𝐶 𝐶𝑊𝐼𝐹
Correlation energy ħ2/𝑚𝜎2
Classical Percolation
Threshold: 𝑉/𝜇 = 1.92
S. Krinner et al., arxiv:1211.7272 (2012)
Thermodynamics
External parameter
(gate potential V)
LDA:
Gibbs-Duhem:
Intensive quantity
(temp. T, pressure P)
𝜇(𝑟) = 𝜇0 − 𝑉(𝑟) → 𝑑𝜇 = −𝑑𝑉
𝑛 𝜇, 𝑇0 𝑑𝜇 = 𝑑𝑃 → 𝑃 = −
𝑛(𝑉, 𝑇0 ) 𝑑𝑉
measure
• Transform gate potential into pressure
«pressure thermometer»
Ku et. al., Science 335, 563-567 (2012)
What is Resistance ?
Normal conductor
Limit of ballistic conductor
R≠0
R=0
U
I=
R
R→0
?
I→∞
Landauer Approach
What is Resistance ?
Landauer Approach – Conduction as Transmission
𝑉
𝜇
𝜇 − 𝑒𝑉
R=0
• Conduction is transmission from one reservoir to the other.
• Prediction: finite resistance for a perfect conductor !
Imry, Landauer
Rev. Mod. Phys. 71, S306–S312 (1999)
Ohmic conduction
• Current at each point in
time
• Slope gives cond. G
• 2 different confinements
3.2 and 3.9 kHz
Ultracold Fermi gases: Vortices
Current
101 Years ago…
Resistance
«Mercury practically zero»
Delft, Kes
Physics Today 63, 38-42 (2010)
Temperature
• Kamerlingh-Onnes observes «unmeasurably
small resistance»
 Discovery of «superconductivity»
• But: no such measurements in ultracold Fermi gases!
Looking in-situ
Intrinsic transport property
Thermodynamic scale
Drift velocity
Pressure
𝑉𝑑 = 𝐼/𝑛𝑙
𝑃=−
𝑛(𝑉, 𝑇0 ) 𝑑𝑉
Ku, Science 335, 563-567 (2012)
Nascimbène, Nature 463, 1057-1060 (2010)
Looking in-situ
Intrinsic transport property
Thermodynamic scale
Drift velocity
Normalized Pressure
𝑉𝑑 = 𝐼/𝑛𝑙
𝑃
𝑃0
Ideal 2d Fermi gas
Ku, Science 335, 563-567 (2012)
Nascimbène, Nature 463, 1057-1060 (2010)