CUA/ITAMP WORKSHOP

Beyond BEC: Ultracold Atoms beyond Mean-Field Physics

November 2-3, 2001

Organizers: James Anglin, Kate Kirby, Daniel Kleppner, Mikhail Lukin


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Online Talks

Bloch

Chapman

 Chuang

DeMille 

 Demler

 Girardeau

 Gunn

 Ho

 Holland

 Kasevich

 Khaykovich

 Moelmer

 Olshanii

 Pethick

 Pritchard

 Sachdev

 Schmiedmayer

 Shlyapnikov

 Stringari

 Thomas

 Thywissen

 Timmermans

 Törmä

 Zoller

Participants

Dr James Anglin
MIT, 26-251
77 Massachusetts Ave.
Cambridge, MA 02139
janglin@mit.edu


Dr. Immanuel Bloch
LMU Muenchen/MPQ for Quantum Optics
Sektion Physik/LS Haensch
Schellingstr. 4/III
80799 Munich, Germany
imb@mpq.mpg.de
Prof Michael S. Chapman
School of Physics
Georgia Institute of Technology
837 State Street
Atlanta, GA 30332-0430
michael.chapman@physics.gatech.edu
Prof Ike Chuang
Massachusetts Institute of Technology
Department of Physics
Cambridge, MA 02138
ichuang@media.mit.edu
Prof Eugene Demler
Harvard University
Physics Department
Cambridge, MA 02138
demler@physics.harvard.edu

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Prof Ivan Deutsch
Dept. of Physics and Astronomy
University of New Mexico
Albuquerque, NM 87131
ideutsch@tangelo.phys.unm.edu
Prof Marvin D. Girardeau
University of Arizona
Optical Sciences Center
Meinel Building
1630 E. University Blvd.
Tucson, AZ 85721
girardeau@optics.arizona.edu
Prof Mike Gunn
School of Physics and Astronomy
University of Birmingham
Edgbaston, Birmingham,
B15 2TT, United Kingdom
jmfg@thsun7.ph.bham.ac.uk
Prof Tin-Lun Ho
Department of Physics
4188 Smith Lab
Ohio State University
Columbus, OH 43210-1106
ho@mps.ohio-state.edu
Prof. Murray Holland
JILA
University of Colorado, Boulder, 440
Boulder, CO 80309-0440
murray.holland@colorado.edu
Prof. Randy Hulet
Rice University
Dept. of Physics and Astronomy, MS61
Houston, TX 77251
randy@atomcool.rice.edu
Prof Mark Kasevich
Department of Physics
Yale University
New Haven, CT 06520-8120
kasevich@amo.physics.yale.edu
Dr. Lev Khaykovich
Laboratoire Kastler Brossel de l'ENS,
24 rue Lhomond,
75231, Paris Cedex 05
Lev.Khaykovich@lkb.ens.fr
Dr Kate Kirby
ITAMP
60 Garden Street, MS 14
Cambridge, MA 02138
Kkirby@cfa.harvard.edu

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Prof Wolfgang Ketterle
Massachusetts Institute of Technology
Department of Physics, 26-243
Cambridge, MA 02139
ketterle@mit.edu
Prof Daniel Kleppner
Massachusetts Institute of Technology
Department of Physics, 26-237
Cambridge, MA 02138
kleppner@mit.edu
Prof Mikhail Lukin
Harvard University
Physics Department
Cambridge, MA 02138
mlukin@cfa.harvard.edu
Prof Klaus Moelmer
Institute of Physics and Astronomy
University of Aarhus
DK 8000 Aarhus C., Denmark
moelmer@ifa.au.dk
Prof Maxim Olshanii
Dept. of Physics and Astronomy
University of Southern California
Los Angeles, CA 90089-0484
olshanii@physics.usc.edu
Prof Chris J. Pethick
NORDITA
Blegdamsvej 17
DK-2100 Copenhagen Oe
Denmark
pethick@nordita.dk

Prof. Mara Prentiss
Harvard University
Physics Department
Cambridge, MA 02138
Mara@atomsun
Prof. David E. Pritchard
Massachusetts Institute of Technology
Department of Physics 26-241
Cambridge, MA 02139
dpritch@MIT.EDU

Prof Subir Sachdev
Yale University
Department of Physics
New Haven CT 06520-8120
subir.sachdev@yale.edu


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Prof Joerg Schmiedmayer
Physikalisches Institut
Universität Heidelberg
D-69117 Heidelberg,Germany
joerg.schmiedmayer@physik.uni-heidelberg.de
Prof Georgy V. Shlyapnikov
FOM Institute AMOLF
Kruislaan 407
1098 SJ, Amsterdam, The Netherlands
shlyapnikov@amolf.nl
Prof Sandro Stringari
Dipartimento di Fisica,
Universita' di Trento
38050 Povo, Italy
stringar@science.unitn.it
Prof John E. Thomas
Department of Physics
Box 90305
Duke University
Durham, NC 27708-0305
jet@phy.duke.edu
Dr. Joseph H. Thywissen
Groupe Optique Atomique
Institut d'Optique
Bat 503, BP 147
91403 ORSAY, France
joseph.thywissen@iota.u-psud.fr
Dr Eddy Timmermans
T-4, MS B-268
Los Alamos National Laboratory
Los Alamos, NM 87545
eddy@t4.lanl.gov
Prof Päivi Törmä
Department of Physics
University of Jyväskylä
P.O.Box 35
FIN-40351 Jyväskylä, Finland
paivi.torma@hut.fi
Prof Peter Zoller
Institute for Theoretical Physics
University of Innsbruck
6020 Innsbruck, Austria
peter.zoller@uibk.ac.at

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Schedule

 Friday, Nov. 2, 2001

Saturday, Nov. 3, 2001

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  Thursday, November 1, 2001

 1:00 - 5:00 p.m.

 Lab tours will be arranged for participants arriving early

 6:00 p.m.

 Informal dinner arrangements

 Friday, November 2, 2001
(All sessions in Phillips Conference Room)

 8:30 a.m.

Coffee, welcome, keynote address

Session I: Low Dimensions

9:00 - 9:50 a.m.

Tutorial Lecture:

S. Stringari: BEC in Low Dimensions

10:00 - 10:50 a.m.

Brief Presentations - Panel:

M. Olshanii: One-Dimensional Physics in Atom Traps

G. Shlyapnikov: Low-Dimensional Trapped Gases

M. Girardeau: Correlation and Interference in Strongly Interacting Quasi-1D Bose Gases

D. Pritchard: Flowing BEC's in Waveguides

J. Thywissen: Towards Bragg Spectroscopy of Quasi-Condensates

11:00 - 12: 00 noon

General discussion: M. Prentiss

 12:00 - 2:00 p.m.

 Lunch, informal discussion

Session II: Quantum Phase Transitions

 2:00 - 2:50 p.m.

Tutorial Lecture:

S. Sachdev: Quantum Phase Transitions in Atomic Gases and Condensed Matter

3:00 - 3:50 p.m.

Brief presentations - Panel:

E. Demler: Spinor Bosonic Atoms in Optical Lattices

M. Gunn: Quantum Vortex Liquids and Composites in Rotating BECs

T-L. Ho

M. Kasevich

I. Bloch: Quantum Phase Transition from a Superfluid to a Mott Insulator in a Gas of Ultracold Atoms

 4:00 - 5:00 p.m.

General discussion: W. Ketterle

 5:30 - 7:30 p.m.

 Buffet Reception in Perkin Lobby and Pratt Conference Room

   

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Saturday, November 3, 2001
(All sessions in Phillips Conference Room)

 8:30 - 9:00 a.m.

Coffee

Session III: Degenerate Fermions

 9:00 - 9:50 a.m.

Tutorial Lecture:

E. Timmermans: Atom-Trap Fermion Superfluidity -- A New Quest?

10:00 - 10:50 a.m.

Brief Presentations - Panel :

C. Pethick: Effects of Correlations on the Transition to a Superfluid State

P. Törmä: Vortices and Josephson Effect in Superfluid Atomic Fermi-Gases

M. Holland: A Theory of Resonance Superfluidity in a Quantum Fermi Gas

J. Thomas: Evaporative Cooling of a Two-Component 6LI Fermi Gas in a Stable CO2 Laser Trap

L. Khaykovich: BEC in a Fermi Sea: When Sympathetic Cooling Stops?

11:00 - 12:00 noon

General Discussion: R.Hulet

 12:00 - 2:00 p.m.

 Lunch, informal discussion

Session IV: Quantum Information

 2:00 - 2:50 p.m.

Tutorial Lecture: P. Zoller

 3:00 - 3:50 p.m.

Brief Presentations - Panel

K.Moelmer: Things To Do with a Hay Stack, If You Cannot Find Your Qubits

I. Chuang

I. Deutsch: A Quantum Computer Is a Many-Body Atomic Clock

J. Schmiedmayer: Implementing Quantum Information Processing with Neutral Atoms on Atom Chips

M. Chapman: Scalable Cavity QED with Trapped Atoms

4:00 - 5:00 p.m. General Discussion (M. Lukin); Summary/Assessment

 5:00 - 6:00 p.m.

Discussion leaders summarize, final discussion, feedback on workshop format (J. Anglin)

 6:00 p.m.

 Informal dinner arrangements

Sunday, November 4, 2001

11:00 a.m. -
4 p.m.

Informal arrangements for discussion or recreation

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Abstracts

Bloch

Chapman

 Chuang

Demler 

Deutsch 

 Girardeau

 Gunn

 Ho

 Holland

 Kasevich

 Khaykovich

 Moelmer

 Olshanii

 Pethick

 Pritchard

 Sachdev

 Schmiedmayer

 Shlyapnikov

 Stringari

 Thomas

 Thywissen

 Timmermans

 Törmä

 Zoller

 

 Quantum Phase Transition from a Superfluid to a Mott Insulator
in a Gas of Ultracold Atoms

Immanuel Bloch

LMU Muenchen/MPQ for Quantum Optics
Sektion Physik/LS Haensch
Schellingstr. 4/III
80799 Munich, Germany

Although in a classical system the ability to change configuration is frozen out at absolute zero temperature, this is not true for a quantum mechanical system. Here fundamental quantum fluctuations are able to induce a phase transition between two ground states of the system as the relative strength of two competing terms in the underlying Hamiltonian is changed. In my talk I will present our recent results on such a quantum phase transition that occurs, when atoms from a Bose-Einstein condensate are loaded into a three-dimensional optical lattice potential. For low potential depths, the atoms form a superfluid phase, in which each atom is spread out over the entire lattice, with perfect phase coherence across the lattice. For high potential depths the repulsive interactions between the atoms cause a transition to a Mott insulator phase. In this phase the atoms are localized to lattice sites with an exactly defined atom number and therefore no phase coherence is present. This Mott insulator phase is characterized by a gap in the excitation spectrum, which is detected in the experiment. Furthermore, we demonstrate that it is possible to reversibly change between the two ground states of the system.

 Scalable Cavity QED with Trapped Atoms

Michael S. Chapman

School of Physics
Georgia Institute of Technology
Atlanta, GA 30332-0430

Cavity QED systems with atoms offer rich versatility for quantum information applications and have been used to demonstrate atom-atom, atom-photon and photon-photon entanglements. Additionally, these systems have applications as very efficient single atom detectors, and as generators of single photon Fock states and other non-classical states.

Developing these systems beyond the proof of principal stage requires integrating the cavity QED systems with robust atom trapping technologies. I will give a brief overview of the near-term experimental prospects for cavity-QED based quantum information protocols, and discuss some of the more outstanding challenges.

 Quantum Computation with NMR: Past, Present, and Future

I. Chuang

Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139

Nuclear spins make remarkably good quantum bits. Today, we have controllable three, five, and seven qubit NMR quantum systems. What has made this possible was the development of methods for readily initializing spins in molecules to states which behave as logical zeros. These molecules produce signals as if they were at zero temperature, while actually being at a very high temperature. Current implementations of such "computational cooling" techniques are limited to ten or so qubits, but interestingly, generalizations have been developed which allow efficient scaling. I will describe the NMR quantum computation experiments we have performed to demonstrate basic quantum algorithms, and suggest how they may provide invaluable guidance for a wide variety of future quantum computer implementations.

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 Spinor Bosonic Atoms in Optical Lattices

Eugene Demler

Harvard University
Physics Department
Cambridge, MA 02138

We examine the problem of Bose F=1 atoms with antiferromagnetic interaction in optical lattices. We argue that several superfluid and Mott insulator phases may occur in this system at low temperatures, including a usual polar condensate phase, a condensate of singlet pairs, a crystal spin nematic phase, and a spin singlet crystal phase. Possibility of experimental observation of these phases is discussed.

 

 A Quantum Computer Is a Many-Body Atomic Clock

Ivan Deutsch

Dept. of Physics and Astronomy
University of New Mexico
Albuquerque, NM 87131

A quantum computer works through interference of many computational paths. These paths are in the abstract Hilbert space associated with a collection of entangled particles, rather than the physical paths of a classical interference pattern, such as a diffraction grating. Thus, a quantum computer can be viewed as a multiparticle Ramsey interferometer. At the single particle level, this is behind the workings of an atomic clock, the most quantum coherent device ever created. A future quantum computer can build upon this success. Implementation will be a grand challenge for theoretical and experimental science and engineering. Many tools are currently or nearly in place - state preparation through atom cooling, coherent control through laser/microwave spectroscopy, measurement through monitored quantum jumps. In order to make progress towards the ultimate goal, we must focus attention on laboratory development of these control tools, must crucially two-qubit quantum logic gates. For atoms, this is effectively the problem of coherent control of a dimer. This is the newest ingredient beyond that common employed in atomic clocks and analogous systems. Optical lattices provide an excellent arena in which to begin implementing these building blocks, with promise of scalability and parallelism necessary for ultimate fault-tolerant operation.

 Correlation and Interference in Strongly Interacting
Quasi-1D Bose Gases

Marvin D. Girardeau

University of Arizona
Optical Sciences Center
Tucson, AZ 85721

The issue that will be raised is the question of visibility of interference fringes (or lack of visibility) in an atom interferometer near the Tonks limit (narrow waveguide with lowest transverse excitation energy large compared with longitudinal zero-point and thermal energies, and scattering length so large that reflection is specular). Exact calculations have already shown that interference is strongly inhibited in an adiabatically split and recombined Tonks gas due to fermionization and differing phases of different Fermi orbitals involved in the Fermi-Bose mapping. This raises two questions: (1) Does such inhibition also occur in, for example, a Tonks double-Y "waveguide on a chip" interferometer? (2) Starting with a waveguide adequately described by a standard BEC/effective field approach (smaller scattering length and/or many accessible transverse modes), how rapidly do interference effects degrade as the transverse frequency is raised and the Tonks limit is approached?

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 Quantum Vortex Liquids and Composites in Rotating BECs

Mike Gunn

School of Physics and Astronomy
University of Birmingham
Edgbaston, Birmingham,
B15 2TT, United Kingdom

Mean-field vortex lattices may be destroyed and correlated states can be produced in rotating BECs by either small numbers of particles or a large amount of angular momentum per particle. These mesoscopic and rapidly rotating limits lead to bose-vortex composite condensation and to Laughlin and cluster (Read-Rezayi) states respectively. Estimates show that the observability of these effects are likely to more practical in traps containing 1000 or fewer particles. No vortices are predicted in the case of attractive interactions.

 Non-Mean-Field Ground States in Dilute Bose Gases

T-L. Ho

Department of Physics
Ohio State University
Columbus, OH 43210-1106

We shall discuss the origin of non-mean field ground states in dilute Bose gases. To illustrate some of these mechanisms, which are related to symmetry and degeneracy of the system, we discuss the crossover from mean-field to non-mean-field ground states in spinor Bose gas, double well/optical lattice systems, and rotating Bose gas. We shall discuss the signatures of these non-mean-field ground states and the parameter range for their existence.

Another mechanism for non-mean-field ground state is strong interaction. We illustrate this by considering the metastable state of a repulsive Bose gas as it approaches Feshbach resonance. We show how interaction effects strongly deplete the atomic and molecular condensate near the resonance, causing the system to ``Fermionize". We shall also discuss the signature of this ``Fermionization".

 A Theory of Resonance Superfluidity in a Quantum Fermi Gas

Murray Holland

JILA
University of Colorado, Boulder, 440
Boulder, CO 80309-0440

I will consider the superfluid phase transition that arises when a Feshbach resonance pairing occurs in a dilute Fermi gas. Considering a specific resonance in potassium-40, this theory predicts that for achievable experimental conditions, the transition to a superfluid phase may be possible at a high critical temperature approaching half the Fermi temperature. Observation of superfluidity in this regime would provide the opportunity to experimentally study the crossover from the momentum correlated superfluidity of weakly-coupled fermions to the Bose-Einstein condensation of strongly-bound composite bosons. I will also discuss a direct and observable signature of the superfluid transition by applying the theory to a gas confined in a harmonic potential. The signature of the phase transition is given by a significant increase in density observed in the vicinity of the trap center. This increase in density is due to the difference in compressibility of the superfluid and normal phases.

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 Heisenberg Spectroscopy in an Optical Lattice

Mark Kasevich

Department of Physics
Yale University
New Haven, CT 06520-8120

We have previously studied the ground state properties of weakly interacting bosonic atoms in a 1-d optical lattice. In particular, we have shown that by controlling the relative strength of the on-site mean-field interaction to the tunneling rate, that on-site number fluctuations are suppressed below those associated with Poissonian statistics. In this past work, we were able to demonstrate 15 dB number squeezing with ~ 103 atoms per site. These states are non-trivial entangled states which may have application in the areas of quantum information or precision spectroscopy. At the extreme parameters of these studies, the lattice was expected to have partially transitioned to an insulating regime, where the quantum state at each site is nearly a Fock state (in recent work we have achieved conditions consistent with bringing the entire lattice through the insulating transition).

We have recently extended this work to study the dynamic evolution of these states under sudden changes in the system parameters, as well as the system response to phase shifts induced by external forces. We have shown that it is possible to induce lattice state oscillations from Fock states to states with well-defined relative phases under appropriate conditions. We will present recent experimental efforts to exploit these responses to implement a Heisenberg-limited interferometric measurement of g, the acceleration due to gravity.

 BEC in a Fermi Sea: When Does Sympathetic Cooling Stop?

L. Khaykovich, F. Schreck, G. Ferrari
T. Bourdel, J. Cubizolles, K.L. Corwin, and C. Salomon

Laboratoire Kastler Brossel
Ecole Normale Supérieure
Paris, France

Recently we have reached a regime of simultaneous quantum degeneracy in a mixture of magnetically trapped Bose and Fermi gases [F. Schreck et al., PRL 87, 080403 (2001)]. A stable 7Li Bose-Einstein condensate (BEC) was produced by thermal contact with a 6Li Fermi gas at a temperature of 1/5 of the Fermi temperature. The question that we would like to raise is, What are the limits of this BEC-Fermi gas cooling scheme?

When the critical temperature (TC) bosons is reached, the typical double structure in the atomic density distribution appears: a strong peak in the center forms the condensate, surrounded by a much broader distribution, the thermal cloud. As the Fermi distribution is very insensitive to temperature, this thermal cloud is used as a thermometer to determine the common temperature. However when the temperature decreases below 0.2 TC, the thermal cloud becomes undetectable and thus brings a technical limit to our measurements. Therefore development of a new thermometry is crucial for researching theoretically predicted and only partially investigated limits such as Pauli blocking of collisions, phase separation, superfluidity of the condensate and heating of the degenerate Fermi gas due to finite lifetime of atoms in the trap. In the talk these limits and their consequences for future work with Fermi gases and possible observation of a BCS transition in 6Li will be discussed.

 Things To Do with a Hay Stack, If You Cannot Find Your Qubits

Klaus Moelmer

Institute of Physics and Astronomy
University of Aarhus
DK 8000 Aarhus C., Denmark

Proposals for quantum information processing with cold atoms involve specific interaction mechanisms which may be difficult to induce in practice at the level of single qubits (atoms) and qubit pairs. We present examples that show how some of these proposals, without access to individual atoms, can be modified to control collective variables of the entire system. This is not sufficient to implement mathematical algorithms, but it provides perspectives for a bright near future for collective quantum states of atoms, e.g., multi-particle entangled states with potential applications for continuous variable data operations, squeezed states with useful noise properties, and specific purpose quantum computing tasks such as simulations on quantum spin systems.

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 One-Dimensional Physics in Atom Traps

Maxim Olshanii

Dept. of Physics and Astronomy
University of Southern California
Los Angeles, CA 90089-0484

One-dimensional Bose gas is a unique example of a simple tractable many-body system with strong interparticles correlations. In this presentation I am going to discuss the experimental accessibility of the strong correlation features, such as the fermionic density profile and 1/sqrt(momentum) peak in the momentum distribution. As most of the current
experimental efforts in this area address the intermediate between weak (mean-field) and strong (Tonks-Girardeau) correlation regime my presentation will focused mainly on the finite coupling strength case, more difficult from the theoretical point of view as compare to the infinitely strong interaction case.

* M. Girardeau , J. Math. Phys. (N.Y.) 1, 516 (1960);
Phys. Rev. 139, B500 ( 1965).

* M. Olshanii, Atomic scattering in the presence of an external
confinement and a gas of impenetrable bosons, Phys. Rev. Lett. 81, 938
(1998)

* Vanja Dunjko, Vincent Lorent, and Maxim Olshanii, Bosons in
cigar-shape
traps: Thomas-Fermi regime, Tonks-Girardeau regime, and in between,
Phys. Rev. Lett., 86, 5413 (2001)

* M. D. Girardeau and E. M. Wright, Measurement of One-Particle
Correlations and Momentum Distributions for Trapped 1D Gases,
Phys. Rev. Lett., 87, 050403 (2001).

 Effects of Correlations on the Transition to a Superfluid State

Chris J. Pethick

NORDITA
Blegdamsvej 17
DK-2100 Copenhagen Oe, Denmark

I shall discuss a number of topics related to the superfluid transition in dilute atomic gases. There are two ways of trying to increase the transition temperature. One is by exchange of low-energy bosons between two fermions. The boson could be, for example, a sound wave in the Fermi gas or in a Bose gas coexisting with the fermions. Such exchanges could lead to a large change in the effective attraction is the system were close to an instability where the compressibility becomes infinite. Calculations by H. Heiselberg (Phys. Rev. A63, 043606 (2001)) suggest that for a two-component Fermi system, there is not such an instability. Another route to making a high transition temperature is to have a soft excitation in the particle-particle channel, as, for example, in the case of a Feshbach resonance. I shall discuss the behavior of the transition temperature as the energy of the Feshbach resonance is changed. If it lies well below zero energy, the system behaves at low temperature as a collection of molecules, while if it is well above twice the Fermi energy, the system behaves as a BCS superfluid. I shall emphasize the role of thermally excited molecules in limiting the transition temperatures that can be achieved.

 Flowing BEC's in Waveguides

David E. Pritchard

Massachusetts Institute of Technology
Department of Physics 26-241
Cambridge, MA 02139

I will discuss waveguides - how to think of the quantum flow problem, and a suggestion about how to observe the transition from Tonks gas to 1-d BEC by looking at the flow versus energy above a soft barrier. I will also mention some practical problems associated with using 10gauss fields transverse to the waveguide to create a field zero and then expecting to control the longitudinal kinetic energy within tens of milligauss (times a bohr magneton).

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 Quantum Phase Transitions in Atomic Gases and Condensed Matter

Subir Sachdev

Yale University
P.O. Box 208120
New Haven CT 06520-8120

I will begin with a simple introduction to quantum phase transitions: what are they and why are they interesting ? I will argue that the study of quantum phase transitions provides powerful tool and a precise language for describing many-body quantum systems in a strong interaction regime. I will then move on to a tutorial description of the simplest system which exhibits a quantum phase transition --- the quantum Ising chain. I will described the nature of the ground state on either side of the critical point, the general applicability of a quasi-particle description of excitations, and the breakdown of the quasi-particle picture near the critical point. These insights lead to a "universal" crossover phase diagram at non-zero temperatures which will be highlighted. Similar paradigms will be shown to apply to more complex systems of experimental interest, like the superfluid-insulator transition. Finally, I will discuss more exotic quantum phase transitions, which are not described by a conventional "order parameter": these usually involve the deconfinement of novel "fractionalized" excitations.

 Implementing Quantum Information Processing with
Neutral Atoms on Atom Chips

Jörg Schmiedmayer

Physikalisches Institut
Universität Heidelberg
Philosophenweg 12
Heidelberg, Germany

Neutral-atom manipulation using integrated micro-devices (Atom Chips) is a new promising experimental approach to QIPC. It combines the best of two worlds: The ability to use cold atoms - a well controllable quantum system where many implementations of QIPC were proposed, and the immense technological capabilities of nano fabrication and microelectronics to manipulate the atoms. A final integrated Atom Chip, will have a reliable source of cold atoms with an efficient loading mechanism, coherent transportation and manipulation of atoms at the nano-scale allowing controlled creation of entanglement, and extremely high resolution light fields and electrodes for the manipulation and internal state sensitive detection of qubits. In my presentation I will highlight the present status of Atom Chip technology, its implementation in experiments, highlight its promises and unknowns, and try to show which research will be necessary to critically assess this road to implementing robust QIPC.

 Low-Dimensional Trapped Gases

Georgy V. Shlyapnikov

FOM Institute AMOLF
Kruislaan 407
1098 SJ, Amsterdam, The Netherlands

I will discuss regimes of quasicondensates in (finite-temperature) 2D and 1D trapped gases. It will be shown that in the 2D case the regime of quasicondensation requires a very large gaseous sample. I will then discuss possibilities for the experimental realization of this regime.

The discussion of the 1D case, will make a (very) brief overview of our theoretical results on quasiBEC in finite-temperature 1D trapped gases and Hannover experimental results on phase-fluctuating condensates in 3D elongated traps. I will then focus attention on vacuum (quantum) fluctuations of the phase. In most cases, at zero temperature one expects the (long) size of the sample to be much smaller than the Haldein phase coherence length. Therefore, the equilibrium state should be a true condensate. I will address the question of what really is "zero temperature"(?), under which conditions the vacuum fluctuations dominate over the thermal fluctuations of the phase(?), and whether one can observe the "Haldein quasicondensate" in experiments with 1D trapped gases(?).

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 BEC in Low Dimensions

Sandro Stringari

Dipartimento di Fisica,
Universita' di Trento
38050 Povo, Italy

In the talk I will first briefly review some exact results of statistical mechanics (Hohenberg-Mermin-Wagner theorem and its extension to zero temperature).

I will then address the question of the behaviour of elementary excitations in the presence of harmonic traps with tight radial confinement, including the 3D cigar and the Tonks gas. I will then discuss the behaviour of 1D arrays of condensates generated by optical lattices. Special emphasis will be given to interference effects during the expansion, the behaviour of the critical temperature and of the axial oscillations which exhibit important Josephson features.

General considerations on the signature of long-range order in the momentum distribution and its measurability in trapped condensates via Bragg spectroscopy will be finally addressed, introducing some of the topics discussed in the other presentations of the session.

 Evaporative Cooling of a Two-component 6Li Fermi
Gas in a Stable CO2 Laser Trap

J.E. Thomas

Department of Physics
Box 90305
Duke University
Durham, NC 27708-0305

We demonstrate in situ evaporative cooling of an optically trapped mixture of the |1/2,±1/2Ò states of 6Li fermions to the degenerate regime. Since this mixture is stable and exhibits a Feshbach resonance, it is well suited for studies of resonance superfluidity as predicted recently. The atoms are confined in a stable single beam CO2 laser trap which achieves a lifetime of up to 500 seconds with a very low residual heating rate. Prior to forced evaporation by lowering the trap depth, initial phase space densities of up to 6 ¥ 10-3 per state are obtained. Temperatures below the Fermi temperature are achieved after 30 seconds of evaporation by lowering the trap depth followed by recompression to full trap depth. Since the scattering length for the trapped mixture is zero at zero magnetic field, evaporation is initiated by applying a bias field which enables interactions to be turned on and off at will. Results for the phase space density versus trap depth will be compared to a scaling law we have derived for evaporation in adiabatically lowered optical traps.

 Towards Bragg Spectroscopy of Quasi-Condensates

Joseph H. Thywissen

Groupe Optique Atomique
Institut d'Optique
Bat 503, BP 147
91403 ORSAY, France

We present measurements in progress of the coherence properties of condensates and quasi-condensates. Using an iron-core electromagnet, we have trapped Rb87 (quasi?)condensates with aspect ratios of up to 390:1, and measured transverse oscillation frequencies as high as 960Hz. We have recently observed Bragg scattering along the long (dipole) axis of the trap, and plan to use Bragg spectroscopy to measure directly the longitudinal coherence length of ultracold clouds as a function of temperature and number of trapped atoms.

 Atom-Trap Fermion Superfluidity -- A New Quest?

Eddy Timmermans

T-4, MS B-268
Los Alamos National Laboratory
Los Alamos, NM 87545

Since the interest of the panel members centers on the prospect of achieving cold atom fermion superfluidity, I will focus on that aspect of fermion atom trap physics. Tentatively, I plan to divide the tutorial lecture in five sections.

In the introduction, I will address the following questions: What is superfluidity? Why do neutral atom traps provide an interesting environment to study fermion superfluidity? What has been achieved experimentally so far?

In section II, I wish to discuss the description of s-wave Cooper pairing physics. I will introduce the mean-field description that leads to the Bogoliubov-de Gennes equations and derive the 'gap' in the homogeneous system limit. I will also briefly mention renormalization issues and review work on calculating the critical temperature.

Signatures of fermion superfluidity in a neutral atom trap, is the subject of section III.

Section IV, I will devote to reviewing some important challenges faced by the experiments: what are the cooling limits for fermion boson and fermion-fermion mixtures?

Finally I will return to the intriguing prospect of 'varying' the fermion-fermion attraction responsible for the Cooper-instability, and discuss specifically the Feshbach resonance prospect in section V.

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 Vortices and Josephson Effect in Superfluid Atomic Fermi-gases

Päivi Törmä

Department of Physics
University of Jyväskylä
FIN-40351 Jyväskylä, Finland

We consider a superfluid of trapped fermionic atoms and study the single vortex solution in the Ginzburg-Landau regime [1]. We define simple analytical estimates for the main characteristics of the system, such as the vortex core size and temperature regimes for the existence of a vortex. The parameter dependence of the vortex core size (healing length) is found to be essentially different form that of the healing length in metallic superconductors or in trapped atomic BEC in the Thomas-Fermi limit. This is an indication of the importance of the confining geometry for the properties of fermionic superfluids.

We also consider the Josephson effect in superfluid atomic Fermi-gases [2]. Four different hyperfine states of the atoms are assumed to be trapped and to form two superfluids by BCS-type pairing. We show that Josephson oscillations can be realized by coupling the superfluids by a laser. By choosing the laser detunings in a suitable way one can create an asymmetric situation which has not been realized in the context of metallic superconductors. This asymmetry in energies allows to resolve the temporal coherence of the order parameter.

 Peter Zoller

Institute for Theoretical Physics
University of Innsbruck
6020 Innsbruck, Austria

This tutorial will focus on implementation of quantum information with quantum optical systems. Starting from the general requirements of quantum computing, quantum communications and precision measurement we will discuss specific systems and mechanism to engineer entanglement. Our focus will be on cold atoms as a tool in this program. This will include a discussion of both single atoms as information carriers and atomic ensembles. Specific questions to be addressed are various schemes for two-qubit gates (either as a dynamical gate or via geometric phases) and quantum communication with atomic ensembles (quantum repeater and teleportation).

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