quantum phase transition in an atomic bose gas with feshbach resonances m.w.j. romans (utrecht) r.a....
TRANSCRIPT
![Page 1: Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649f585503460f94c7e0fb/html5/thumbnails/1.jpg)
Quantum phase transition in an atomic Bose gas with Feshbach resonances
M.W.J. Romans (Utrecht)
R.A. Duine (Utrecht)
S. Sachdev (Yale)
H.T.C. Stoof (Utrecht)
cond-mat/0312446
See also L. Radzihovsky, J. Park , P. Weichman, cond-mat/0312237.
![Page 2: Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649f585503460f94c7e0fb/html5/thumbnails/2.jpg)
Exotic order in an atomic Bose gas with Feshbach resonances
M.W.J. Romans (Utrecht)
R.A. Duine (Utrecht)
S. Sachdev (Yale)
H.T.C. Stoof (Utrecht)
cond-mat/0312446
See also L. Radzihovsky, J. Park , P. Weichman, cond-mat/0312237.
![Page 3: Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649f585503460f94c7e0fb/html5/thumbnails/3.jpg)
• When are two quantum states (of an infinite system) really distinct ?• Can we connect two states by adiabatic evolution of a coupling constant ?
![Page 4: Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649f585503460f94c7e0fb/html5/thumbnails/4.jpg)
• When are two quantum states (of an infinite system) really distinct ?• Can we connect two states by adiabatic evolution of a coupling constant ?
If not, then the two states are separated by a quantum phase transition(s)
![Page 5: Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649f585503460f94c7e0fb/html5/thumbnails/5.jpg)
• When are two quantum states (of an infinite system) really distinct ?• Can we connect two states by adiabatic evolution of a coupling constant ?
If not, then the two states are separated by a quantum phase transition(s)
A quantum phase transition must occur if the states have
• distinct “conventional” order parameters/broken symmetry
• distinct “quantum/topological/exotic” order with distinct quantum numbers of excitations
![Page 6: Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649f585503460f94c7e0fb/html5/thumbnails/6.jpg)
Fermi gas near a Feshbach resonance
BEC of molecules
BCS state of paired fermions
detuning
![Page 7: Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649f585503460f94c7e0fb/html5/thumbnails/7.jpg)
Fermi gas near a Feshbach resonance
BEC of molecules
BCS state of paired fermions
pairs ,
Antisym m i ji j
r r
Smooth crossover between two limits;Different theories can be judged only by their quantitative accuracy.
detuning
![Page 8: Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649f585503460f94c7e0fb/html5/thumbnails/8.jpg)
Bose gas near a Feshbach resonance
BEC of molecules BEC of atoms
detuning
![Page 9: Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649f585503460f94c7e0fb/html5/thumbnails/9.jpg)
Bose gas near a Feshbach resonance
BEC of molecules BEC of atoms
pairs ,
Sym m i ji j
r r
atoms a i
i
r
detuning
![Page 10: Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649f585503460f94c7e0fb/html5/thumbnails/10.jpg)
Bose gas near a Feshbach resonance
BEC of molecules BEC of atoms
pairs ,
Sym m i ji j
r r
atoms a i
i
r
P. Nozieres and D. Saint James, J. Physique 43, 1133 (1982) found a sharp transition between two superfluids in a variational calculation
detuning
![Page 11: Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649f585503460f94c7e0fb/html5/thumbnails/11.jpg)
Bose gas near a Feshbach resonance
detuning
BEC of molecules BEC of atoms
pairs ,
Sym m i ji j
r r
atoms a i
i
r
P. Nozieres and D. Saint James, J. Physique 43, 1133 (1982) found a sharp transition between two superfluids in a variational calculation
We (Romans et al. cond-mat/0312446 and Radzihovsky et al. cond-mat/0312337) argued for the necessity of a quantum phase transition between two distinct superfluids which are distinguished by an Ising quantum order.
![Page 12: Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649f585503460f94c7e0fb/html5/thumbnails/12.jpg)
Why are the two superfluids distinct ?
2
h
e
2
h
e
h
e
h
e
Vortices in a molecular superfluidVortices in a molecular superfluid
![Page 13: Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649f585503460f94c7e0fb/html5/thumbnails/13.jpg)
Why are the two superfluids distinct ?
2
h
e
m
2ime
2
h
e
h
e
h
e
Vortices in a molecular superfluidVortices in a molecular superfluid
![Page 14: Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649f585503460f94c7e0fb/html5/thumbnails/14.jpg)
Why are the two superfluids distinct ?
2
h
e
m
2ime
2
h
e
h
e
h
e
Vortices in a molecular superfluidVortices in a molecular superfluid
m
4ime
![Page 15: Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649f585503460f94c7e0fb/html5/thumbnails/15.jpg)
Why are the two superfluids distinct ?
2
h
e
2
h
e
h
e
h
e
Vortices in an atomic superfluidVortices in an atomic superfluid
![Page 16: Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649f585503460f94c7e0fb/html5/thumbnails/16.jpg)
Why are the two superfluids distinct ?
2
h
e
2
h
e
h
e
h
e
Vortices in an atomic superfluidVortices in an atomic superfluid
,m a
4 2,i im ae e
![Page 17: Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649f585503460f94c7e0fb/html5/thumbnails/17.jpg)
Why are the two superfluids distinct ?
2
h
e
,m a
2 ,i im ae e
2
h
e
h
e
h
e
Vortices in an atomic superfluidVortices in an atomic superfluid
,m a
4 2,i im ae e
![Page 18: Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649f585503460f94c7e0fb/html5/thumbnails/18.jpg)
Why are the two superfluids distinct ?
2
h
e
,m a
2 ,i im ae e
2
h
e
h
e
h
e
Vortices in an atomic superfluidVortices in an atomic superfluid
,m a
4 2,i im ae e
Half vortices are confined in pairs by a ``branch cut’’ which costs a finite energy per unit length
![Page 19: Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649f585503460f94c7e0fb/html5/thumbnails/19.jpg)
Bose gas near a Feshbach resonance
detuning
BEC of molecules BEC of atoms
Half-vorticesfree
Half-vorticesfree
Half-vorticesconfined
Half-vorticesconfined
Confinement-deconfinement transition in the 3d Ising universality class at T>0
![Page 20: Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649f585503460f94c7e0fb/html5/thumbnails/20.jpg)
Bose gas near a Feshbach resonance
Molecular superfluid
Atomic superfluid
Ising transition
Note: transition occurs at negative detuning
![Page 21: Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649f585503460f94c7e0fb/html5/thumbnails/21.jpg)
Bose gas near a Feshbach resonance
Detecting the Ising transition:
• Observation of vortices
• Non-analytic increase in atomic density
• “Critical slowing down” : strong damping of collective modes and decay of atomic density fluctuations into critical fluctuations
Detecting the Ising transition:
• Observation of vortices
• Non-analytic increase in atomic density
• “Critical slowing down” : strong damping of collective modes and decay of atomic density fluctuations into critical fluctuations