Ultracold%20atoms,%20molecules,%20and%20ions:%20Optical%20Lattice%20Emulators%20and%20beyond

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Ultracold atoms, molecules, and ions Optical
Lattice Emulators and beyond
Eugene Demler Harvard University
E. Altman (Weizmann), E. Dalla Torre
(Weizmann), A. Imambekov (Yale), T. Giamarchi
(Geneva), T. Kitagawa (Harvard),S. Pielawa
(Harvard)
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Strongly correlated systems of cold atoms

• Optical lattices

• Feshbach resonances

• Low dimensional systems

• Systems with long range interactions
• (Coulomb interaction for trapped ions,
• dipolar interactions for polar molecules)

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New Era in Cold Atoms Research
Focus on Systems with Strong Interactions
Goals

• Resolve long standing questions in condensed
  matter physics
• (e.g. origin of high temperature
  superconductivity)

• Resolve matter of principle questions
• (e.g. existence of spin liquids in two and
  three dimensions)

• New perspective on strongly correlated systems
• e.g. higher order correlation functions
  revealed in noise
• New phenomena in many-body systems
• e.g. coherent far from equilibrium dynamics

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New Phenomena in quantum many-body systems of
ultracold atoms
Complementary detection schemes- Single shot vs
steady state measurements
Long intrinsic time scales- Interaction energy
and bandwidth 1kHz- System parameters can be
changed over this time scale
Decoupling from external environment- Long
coherence times
Can achieve highly non equilibrium quantum
many-body states
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Higher order correlations revealed in noise
Fluctuations in low dimensional systems
Atom-chip experiments
Interference between independent condensates
Correlations encoded into fringe statistics
Hofferberth et. al. Nature Phys. 2008 (Vienna
group)
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Nonequilibrium dynamics of Hubbard model
Instability of a moving condensate in an
optical lattice
Theory Altman et al. PRL 2005 Experiment Mun
et al. PRL 2007 also Fertig et al. PRL
2004 McKay et al. Nature 2008
Dynamical instability in 3d lattice,
Smearing of instability in 1d lattice,
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Quantum noise as a probe of non-equilibrium
dynamics Ramsey interferometry and many-body
decoherence
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Dynamics in 1d Ramsey interference
Interaction induced collapse of Ramsey fringes.
Spin echo

• Experiments in 1d tubes
• Widera et al.
• PRL (2008)

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Interaction induced collapse of Ramsey fringesin
one dimensional systems
How to distinguish decoherence due to many-body
dynamics?
Luttinger liquid approach
Evolution of spin distribution functions
Only q0 mode shows complete spin echo Finite q
modes continue decay The net visibility is a
result of competition between q0 and other modes
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NEW PERSPECTIVE ON MANY-BODY SYSTEMS

• QUANTUM MANY-BODY SYSTEMS
• IN THE PRESENSE OF
• NONEQUILIBRIUM NOISE

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Question
What happens to low dimensional quantum systems
when they are subjected to external
non-equilibrium noise?
One dimensional Luttinger state can evolve into a
new critical state. This new state has
intriguing interplay of quantum critical and
external noise driven fluctuations
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A brief reviewUniversal long-wavelength theory
of 1D systems
Haldane (81)
Displacement field
Long wavelength density fluctuations (phonons)
Weak interactions K gtgt1Hard core bosons
K 1Strong long range interactions K lt
1
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1D review contd Wigner crystal correlations
Wigner crystal order parameter
No crystalline order !
Scale invariant critical state (Luttinger liquid)
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1D review contdEffect of a weak commensurate
lattice potential
How does the lattice potential change under
rescaling ?
Quantum phase transition Klt2 Pinning by the
lattice (Mott insulator) Kgt2 Critical
phase (Luttinger liquid)
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New systems more prone to external disturbance
Ultracold polar molecules
E
Trapped ions
(from NIST group )
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Linear ion trap
Linear coupling to the noise
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Measured noise spectrum in ion trap
From dependence of heating rate on trap frequency.
f
Monroe group, PRL (06), Chuang group, PRL (08)

• Direct evidence that noise spectrum is 1/f
• Short range spatial correlations ( distance
  from electrodes)

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Ultra cold polar molecules
E
Polarizing electric field
Molecule polarizability
System is subject to electric field noise from
the electrodes !
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Long wavelength description of noisy low D systems
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Effective coupling to external noise
gtgt
The backscattering z can be neglected if the
distance to the noisy electrode is much larger
than the inter-particle spacing.
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Effective harmonic theory of the noisy system
(Quantum) Langevin dynamics
Thermal bath
External noise
Dissipative coupling to bath needed to ensure
steady state (removes the energy pumped in by the
external noise)
Implementation of bath continuous cooling
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Wigner crystal correlations
Case of local 1/f noise

• Decay of crystal correlations remains power-law.
  
• Decay exponent tuned by the 1/f noise power.

1/f noise is a marginal perturbation ! Critical
steady state
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Effect of a weak commensurate lattice potential
Without lattice Scale invariant steady state.
How does the lattice change under a scale
transformation?
Phase transition tuned by noise power
(Supported also by a full RG analysis within the
Keldysh formalism)
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1D-2D transition of coupled tubes
Scaling of the inter-tube hopping
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Global phase diagram
Inter-tube tunneling
Inter-tube interactions
Kc
Kc
Critical state
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2D superfluid
1D critical
2D crystal
1/4
F0 /h
F0 /h
Both perturbations
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SummaryNew perspective on physics of strong
correlationsfrom systems of ultracold atoms,
molecules, ions

• Nonequilibrium dynamics
• Analysis of higher order correlation functions

Example Decay of Ramsey fringes in one
dimensional systems

• Effects of external noise on quantum critical
  states
• new critical state
• new phases and phase transitions tuned by noise

Can be studied with ions and ultracold polar
molecules
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New critical state of 1d systems subject to 1/f
noise

• Decay of crystal correlations remains power-law.
  
• Decay exponent tuned by the 1/f noise power.

• Novel phase transitions tuned by
  acompetition of noise and quantum fluctuations