We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS)
superfluidity to Bose-Einstein condensation (BEC) in a two-dimensional Fermi
gas at T=0 using the fixed-node diffusion Monte Carlo method. We calculate the
equation of state and the gap parameter as a function of the interaction
strength, observing large deviations compared to mean-field predictions. In the
BEC regime our results show the important role of dimer-dimer and atom-dimer
interaction effects that are completely neglected in the mean-field picture.
Results on Tan's contact parameter associated with short-range physics are also
reported along the BCS-BEC crossover.Comment: 4 pages, 4 figure

Bertaina, G.

Giorgini, S.

English

arXiv

We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluidity to Bose-Einstein condensation (BEC) in a two-dimensional Fermi gas at T = 0 using the fixed-node diffusion Monte Carlo method. We calculate the equation of state and the gap parameter as a function of the interaction strength, observing large deviations compared to mean-field predictions. In the BEC regime our results show the important role of dimer-dimer and atom-dimer interaction effects that are completely neglected in the mean-field picture. Results on Tan's contact parameter associated with short-range physics are also reported along the BCS-BEC crossover

Infoscience - École polytechnique fédérale de Lausanne

BCS-BEC Crossover in a Two-Dimensional Fermi Gas

We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluidity to Bose-Einstein condensation (BEC) in a two-dimensional Fermi gas at T=0 using the fixed-node diffusion Monte&nbsp;Carlo method. We calculate the equation of state and the gap parameter as a function of the interaction strength, observing large deviations compared to mean-field predictions. In the BEC regime our results show the important role of dimer-dimer and atom-dimer interaction effects that are completely neglected in the mean-field picture. Results on Tan's contact parameter associated with short-range physics are also reported along the BCS-BEC crossover

Bertaina, G

Giorgini, S

Archivio istituzionale della ricerca - INRIM

BCS-BEC crossover in a two-dimensional Fermi gas

G. Bertaina

S. Giorgini

Crossref

Physical Review Letters

We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluidity to Bose-Einstein condensation (BEC) in a two-dimensional Fermi gas at T=0 using the fixed-node diffusion Monte Carlo method. We calculate the equation of state and the gap parameter as a function of the interaction strength, observing large deviations compared to mean-field predictions. In the BEC regime our results show the important role of dimer-dimer and atom-dimer interaction effects that are completely neglected in the mean-field picture. Results on Tan's contact parameter associated with short-range physics are also reported along the BCS-BEC crossover

AIR Universita degli studi di Milano

We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluidity to Bose-Einstein condensation (BEC) in a two-dimensional Fermi gas at $T=0$ using the fixed-node diffusion Monte Carlo method. We calculate the equation of state and the gap parameter as a function of the interaction strength, observing large deviations compared to mean-field predictions. In the BEC regime our results show the important role of dimer-dimer and atom-dimer interaction effects that are completely neglected in the mean-field picture. Results on Tan's contact parameter associated with short-range physics are also reported along the BCS-BEC crossover

   
BCS-BEC Crossover in a Two 
Dimensional Fermi Gas
Gianluca Bertaina
ITP-EPFL, Lausanne
in collaboration with Prof. Stefano Giorgini
INO-BEC, Trento, Italy
Joint annual meeting of SPS and ÖPG
Lausanne, June 15, 2011
  
Outline
 Ultracold Fermi gases and BCS-BEC crossover
 Quantum Monte Carlo techniques
 BCS-BEC crossover in two dimensions
  
 Short range interaction 
 Diluteness
 Low temperature 
 1) Laser cooling of alkali atoms 
(6Li,40K ...)  
 2) Magneto-optical cooling and 
trapping (two hyperfine states)
 Quantum degeneracy 
 3) Imaging: density and spin density
Ultracold Fermi gases
R≪l
nT
d1
R≪T
R
  
BCS-BEC crossover
2 species of fermions with 
attractive interaction at T=0        
  (Feshbach resonance)
 Weak coupling:                
Cooper instability 
 Strong coupling:          
Condensate of dimers 
 Crossover:                               
no phase transition and no 
small parameter for perturbation 
theory                                      
→ QMC
Ketterle group, MIT (3D system)
E /N~F
E /N~
b
2
  
Diffusion Monte Carlo (DMC)
Bosons : exact (ground state)
Fermions : Fixed Node approx. (variational principle)
−
∂
∂
=H
x T  x0
〈 H 〉= 〈0∣H∣T 〉
〈0∣T 〉
=
∫0x T  x
〈x∣H∣T 〉
T  x
dx
∫0x T x dx
=∫ g x EL x dx
 x ,=e−H T x 
Schroedinger equation in imaginary time
Eigenfunctions nx ,=e
−E nnx 
Random walk + Drift
Basic Algorithm (small time-step expansion)
Branching
Energy
T Trial (guide) wavefunction
  
BCS-BEC crossover in 2D
G. Bertaina and S. Giorgini, Phys. Rev. Lett. 106, 110403 (2011).
Model hamiltonian: Square well interaction (in universal regime nRd <<1)
Trial Wavefunctions (used to fix the nodal surface in DMC):
 Weak coupling:
Jastrow factor: f: two-body problem
 Strong coupling:
       : bound state
a2D∝az exp−2 aza3D 
Optically trapped gas: Quasi-2D 
Experiments (2010): Turlapov, Koehl
az
Mapping: trapped 3D → Pure 2D
 JS x =J  D N D N 
BCS=A[ x11 ' ...xN N  ]
J  =∏
ii '
f   xii ' 

F≪ℏz
b∝−
ℏ2
ma2D
2Bound state
  
BCS-BEC crossover in 2D
G. Bertaina and S. Giorgini, Phys. Rev. Lett. 106, 110403 (2011).
E
N
=E FG−
∣b∣
2
Energy per particle
E
N
=−
b
2

ℏ2nd
md
1
log 1
nd add
2
[12nd order ]
E
N
=E FG1−1 A2 
BCS selfconsistent theory (Randeria)
misses interaction between bosons
Fermi liquid energy functional (small gap)
Composite bosons: add ~ 0.55(4) a2D (Petrov)
= log k F a2DCrossover parameter:
  
BCS-BEC crossover in 2D
G. Bertaina and S. Giorgini, Phys. Rev. Lett. 106, 110403 (2011).
Gap in the spectrum
E N 1,N =E N  , N gap
Short range interactions:
Contact parameter (Tan)
d E
d log k F a2D
∝C
g 
2 r  ∝
r0
C log r /a2D
2
Interpretation:
One fermion in a BEC
aad ~ 1.7(1) a2D
  
Conclusions
QMC shows absolute relevance of beyond mean-field 
corrections
The nodal surface of the used wavefunctions 
contains the relevant T=0 physics
Outlook
Polaron-molecule problem in 2D
Phase separation


BCS-BEC crossover in a two-dimensional Fermi gas

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AIR Universita degli studi di Milano