Schroll, Christian. Decoherence and correlations in systems of trapped ultracold quantum gases. 2005, Doctoral Thesis, University of Basel, Faculty of Science.

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Abstract
Since the achievement of BoseEinstein condensation (BEC), the progress in matterwave
physics has been immense. Among the many recent achievements there is
the miniaturization of atom traps, demonstration of the superfluidMott insulator
quantumphase transition in optical lattices and the experimental demonstration of
the BECBCS crossover in ultracold gases.
Miniaturization of atom traps using microstructured wires on a chip is one important
step towards an onchip coldatom device. These socalled \atom chips" provide
high control and versatility for trapping and guiding the ultracold atomic clouds.
Particularly interesting is the use of these microchips to build mesoscopic devices
for cold atomic clouds as, for instance, in the case of an atomcloud interferometer.
However, these mesoscopic devices require coherent transport of the atom cloud. A
general method to treat decoherence due to current fluctuations in multiwire atomchip
traps is presented in the rst part of this thesis. The decoherence rate Γ shows a
strong dependence on the distance between the wire and the atom cloud, r0, scaling
as Γ ~ r4 0 for a single atom waveguide. Considering an interferometer device, a
strong dependence of the decoherence rate on the trap geometry is found.
Studying manybody eects in ultracold quantum gases is another important
research eld. Experiments using ultracold quantum gases in optical lattices have
demonstrated the superuidMott insulator quantum phase transition and manybody
entanglement. Optical lattices are based on a periodic modulation of the light
intensity, generated by retroreected laser beams. Correlations of the atomic cloud
between dierent lattice sites of the optical lattice play a central role in these manybody
experiments. The dierent phases of the superuidMott insulator system can
be characterized by the dierent behavior of the interlattice site correlations. There
are several numerical methods such as Quantum Monte Carlo (QMC) simulations,
Density Matrix Renormalization Group (DMRG) simulations, exactdiagonalization,
or the Gutzwiller ansatz, to investigate the dynamics of an ultracold gas in an optical
lattice theoretically. The Gutzwiller method, corresponding to the meaneld solution,
allows for the treatment of large lattice sizes. Meaneld approaches have proven
to be very useful to describe manybody physics. However, diculties arise in the correct
description of the behavior of the decay of interlattice site correlations. Based on
the Gutzwiller approach, we have developed a method which allows the successive inclusion
of interlattice site correlations. Comparing the results for the particlenumber
uctuations and the correlation function obtained from pure Gutzwiller calculations,
to calculations which perturbatively include shortrange correlations and calculations
using \quasiexact methods", showed a considerable improvement relative to the pure
Gutzwiller results due to the inclusion of shortrange correlations.
Manybody eects do not only arise in periodic potentials, but become increasingly
important at ultralow temperatures. The formation of BoseEinstein condensates
requires an overlap of the atom wavefunctions and, hence, the formation of
a single condensate wavefunction. Another example of a manybody state is the
superuidBCS state, commonly used as a description of superconductivity. Here,
fermions in dierent hyperne states form Cooper pairs. Experiments with ultracold
quantum gases enable a variation of the interparticle interaction, e.g. , by using
a Feshbach resonance. Using Feshbach resonances to tune the interaction strength
has enabled the experimental observation of the crossover from a superuidBCS
state to a BoseEinstein condensate of molecules. A useful way to characterize the
dierent states of ultracold quantum gases is to investigate the particlenumber uctuations.
In this thesis we suggest to divide the atomic cloud into bins and consider
the atomnumber uctuations in these bins. We calculate the full counting statistics
for dierent physical systems of ultracold gases (e.g. bosonic gases, fermionic gases,
and spin mixtures). In particular, we consider the BCSstate as a rst trial example
to show that there is a strong variation in the particlenumber statistics at the
crossover from a superuidBCS state to a BoseEinstein condensate of molecules.
physics has been immense. Among the many recent achievements there is
the miniaturization of atom traps, demonstration of the superfluidMott insulator
quantumphase transition in optical lattices and the experimental demonstration of
the BECBCS crossover in ultracold gases.
Miniaturization of atom traps using microstructured wires on a chip is one important
step towards an onchip coldatom device. These socalled \atom chips" provide
high control and versatility for trapping and guiding the ultracold atomic clouds.
Particularly interesting is the use of these microchips to build mesoscopic devices
for cold atomic clouds as, for instance, in the case of an atomcloud interferometer.
However, these mesoscopic devices require coherent transport of the atom cloud. A
general method to treat decoherence due to current fluctuations in multiwire atomchip
traps is presented in the rst part of this thesis. The decoherence rate Γ shows a
strong dependence on the distance between the wire and the atom cloud, r0, scaling
as Γ ~ r4 0 for a single atom waveguide. Considering an interferometer device, a
strong dependence of the decoherence rate on the trap geometry is found.
Studying manybody eects in ultracold quantum gases is another important
research eld. Experiments using ultracold quantum gases in optical lattices have
demonstrated the superuidMott insulator quantum phase transition and manybody
entanglement. Optical lattices are based on a periodic modulation of the light
intensity, generated by retroreected laser beams. Correlations of the atomic cloud
between dierent lattice sites of the optical lattice play a central role in these manybody
experiments. The dierent phases of the superuidMott insulator system can
be characterized by the dierent behavior of the interlattice site correlations. There
are several numerical methods such as Quantum Monte Carlo (QMC) simulations,
Density Matrix Renormalization Group (DMRG) simulations, exactdiagonalization,
or the Gutzwiller ansatz, to investigate the dynamics of an ultracold gas in an optical
lattice theoretically. The Gutzwiller method, corresponding to the meaneld solution,
allows for the treatment of large lattice sizes. Meaneld approaches have proven
to be very useful to describe manybody physics. However, diculties arise in the correct
description of the behavior of the decay of interlattice site correlations. Based on
the Gutzwiller approach, we have developed a method which allows the successive inclusion
of interlattice site correlations. Comparing the results for the particlenumber
uctuations and the correlation function obtained from pure Gutzwiller calculations,
to calculations which perturbatively include shortrange correlations and calculations
using \quasiexact methods", showed a considerable improvement relative to the pure
Gutzwiller results due to the inclusion of shortrange correlations.
Manybody eects do not only arise in periodic potentials, but become increasingly
important at ultralow temperatures. The formation of BoseEinstein condensates
requires an overlap of the atom wavefunctions and, hence, the formation of
a single condensate wavefunction. Another example of a manybody state is the
superuidBCS state, commonly used as a description of superconductivity. Here,
fermions in dierent hyperne states form Cooper pairs. Experiments with ultracold
quantum gases enable a variation of the interparticle interaction, e.g. , by using
a Feshbach resonance. Using Feshbach resonances to tune the interaction strength
has enabled the experimental observation of the crossover from a superuidBCS
state to a BoseEinstein condensate of molecules. A useful way to characterize the
dierent states of ultracold quantum gases is to investigate the particlenumber uctuations.
In this thesis we suggest to divide the atomic cloud into bins and consider
the atomnumber uctuations in these bins. We calculate the full counting statistics
for dierent physical systems of ultracold gases (e.g. bosonic gases, fermionic gases,
and spin mixtures). In particular, we consider the BCSstate as a rst trial example
to show that there is a strong variation in the particlenumber statistics at the
crossover from a superuidBCS state to a BoseEinstein condensate of molecules.
Advisors:  Bruder, Christoph 

Committee Members:  Belzig, Wolfgang and Zwerger, W. 
Faculties and Departments:  05 Faculty of Science > Departement Physik > Physik > Theoretische Physik (Bruder) 
UniBasel Contributors:  Bruder, Christoph 
Item Type:  Thesis 
Thesis Subtype:  Doctoral Thesis 
Thesis no:  7268 
Thesis status:  Complete 
Number of Pages:  144 
Language:  English 
Identification Number: 

edoc DOI:  
Last Modified:  22 Jan 2018 15:50 
Deposited On:  13 Feb 2009 15:14 
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