Study of the thermodynamics properties of ultracold Fermi and Bose atomic gases

Project leaders

Giacomo Roati, Vanderlei Salvador Bagnato

Agreement

BRASILE - CNPq - Conselho Nacional Desenvolvimento Cientifico y Tecnologico

Call

CNR/CNPq 2012-2013

Department

Materials and Devices

Thematic area

Physical sciences and technologies of matter

Status of the project

Extended

Report for renewal

joint-report-roati.pdf

Research proposal

In this bilateral CNR-CNPq project we want to investigate the thermodynamics of both Fermi and Bose gases composed by lithium and rubidium atoms respectively. This project will be complementary and the natural extension of our previous proposal dedicated to the out-of-equilibrium systems (see the final report). In the present case, we will be able also to investigate the physics of ultracold fermions showing the peculiar effects of quantum statistics.
I will be the responsible of the lithium experiment that is currently under construction at LENS (European Laboratory for Non-Linear Spectroscopy) laboratories in Florence. LENS has special agreements with INO-CNR, allowing the INO-CNR researchers to benefit of all its experimental facilities.
The rubidium experiment is now running in Brazil in the Sao Carlos laboratories, University of Sao Paolo (USP), under the supervision of Prof. V. Bagnato, the Brazilian PI of this joint CNR-CNPq project.

Our interest in studying the thermodynamics of ultracold atomic system relies on the possibility of addressing many unsolved questions on the fundaments of Fermi and Bose gases that still are under debate in the scientific community, such as the nature of the phase transition to Bose-Einstein condensation, or the validity of the Fermi liquid theory in three and in lower dimensions.
The physical systems at thermal equilibrium are described by some thermodynamic variables, linked by an equation of state (EOS). For example, in the case of a gas of particles the EOS would consist of expressions of pressure and density as functions of temperature T and chemical potential ¼. In the ideal homogeneous case the equation of state is known in any dimension independently both for bosons and fermions [1].
Adding the interactions between the particles, the situation becomes more complex and some approximations must be made in the theory or one has to rely on numerical analysis. The comparison with the experiments is then mandatory to validate the theoretical predictions. In this context, ultracold atoms trapped into harmonic potentials can provide important information, behaving as ideal quantum simulators of many-body phenomena, becoming testing bed of quantum Hamiltonians [2]. In particular, the combination of ultracold atoms and optical potentials has opened up a new way of studying condensed matter problems with higher controllability and unprecedented clarity. Ultracold atoms realize the Richard Feynman idea that the complex aspects of nature would be better simulate by real quantum systems [3]. The equation of state of 3D Fermi gases and for a quasi-2D Bose-Einstein condensate has been recently measured [4, 5]. In these experiments people extract the equation of state by detecting the in-trap density profile of the cold clouds. Local density approximation (LDA) gives criteria to take into account the inhomogeneity due to the trapping potential.

In our project we plan to use a slightly different path to extract the phase diagram. In particular we will rely on the idea proposed by. V. Romero in [6]. In this work it has been pointed out that despite the presence of the harmonic confinement it is still possible to define some global variables that describe the system. This is complementary with the LDA approximation in which it is natural to consider "local" quantity instead of "global" ones.
The inverse of the harmonic trapping frequencies plays the role of the extensive thermodynamic volume V that is connected to the intensive variable that describes the hydrostatic pressure P. Since the knowledge of the trapping frequencies is experimentally accessible, as well as the temperature T, it will be possible to derive the equation of state P (N/V, T).

In the case of bosonic system (CNPq), it will be interesting to characterize the order of the phase transition. This is a delicate issue that it still under debate. In fact while it is clear that the liquid to superfluid transition in 4He is a continuous second order transition, in the case of trapped Bose-Einstein condensates (BEC) there are still some doubts. We want to address this point by extracting the EOS, and determining the isothermal compressibility at the critical temperature. This should provide us information on the order of the phase transition. In fact the divergence of the compressibility close to the critical point will be the smoking gun of the second order nature of such quantum phase transition. We would like also to extend this study to the case of turbulent clouds, determining the thermodynamics variables in this exotic state of matter.

In the case of Fermi gases (INO-CNR), we will concentrate out investigations on the two-dimensional case (2D). In fact 2D fermions are particularly interesting systems and they present some of the most intriguing effects in nature.
The thermodynamics of two-dimensional fermions is still a quite unexplored direction of research, being very interesting though. In particular we would like to study the EOS at finite temperatures and interactions (normal and superfluid regimes). In the normal case, we will want to address the debate about whether the behavior of a quasi-2D Fermi gas above the critical temperature Tc is described by the standard Fermi liquid theory. P. W. Anderson has suggested that the normal phase of high-Tc superconductors may not be correctly caught by the standard Fermi liquid theory. However, there is lot of controversy around this statement and we hope that we can discriminate between different theories with our experimental work.

[1] K. Huang, Statistical Mechanics, Wiley edt.
[2] I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. 80, 885 (2008).
[3] R. Feynman, International Journal of Theoretical Physics, Vol. 21, (1982).
[4] S. Nascimbène et al., Nature 463, 1057-1060 (2010).
[5] T. Yefsah et al. Phys. Rev. Lett. 107, 130401 (2011).
[6] V. Romero-Rochin, Phys. Rev. Lett. 94, 1309610, (2005).
[7] P.W. Anderson, Phys. Rev. Lett. 64, 1839 (1990).

Research goals

1) Study of the equation of state of a Bose-Einstein condensate of rubidium atoms. Determination of the thermodynamic variables that describe the BEC. Addressing the order of the BEC phase-transition in in-homogenously trapped gases.
2) Study of the thermodynamics of a Fermi gas of lithium atoms at different interactions strengths and temperatures in two-dimensional potentials. Comparison of the experimental results with the standard Landau Fermi liquid theory.

Last update: 11/07/2025