Direct observation of the Fermi surface in an ultracold atomic gas

Rapid Communication

Direct observation of the Fermi surface in an ultracold atomic gas

T. E. Drake, Y. Sagi, R. Paudel, J. T. Stewart, J. P. Gaebler, and D. S. Jin

Phys. Rev. A 86, 031601(R) – Published 6 September 2012

Abstract

The ideal (i.e., noninteracting), homogeneous Fermi gas, with its characteristic sharp Fermi surface in the momentum distribution, is a fundamental concept relevant to the behavior of many systems. With trapped Fermi gases of ultracold atoms, one can realize and probe a nearly ideal Fermi gas; however, these systems have a nonuniform density due to the confining potential. We show that the effect of the density variation, which typically washes out any semblance of a Fermi surface step in the momentum distribution, can be mitigated by selectively probing atoms near the center of a trapped gas. With this approach, we have directly measured a Fermi surface in momentum space for a nearly ideal gas, where the average density and temperature of the probed portion of the gas can be determined from the location and sharpness of the Fermi surface.

Received 30 March 2012

DOI:https://doi.org/10.1103/PhysRevA.86.031601

Authors & Affiliations

T. E. Drake, Y. Sagi, R. Paudel, J. T. Stewart, J. P. Gaebler, and D. S. Jin^*

JILA, National Institute of Standards and Technology and the University of Colorado, and the Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA

^*Electronic address: jin@jilau1.colorado.edu; URL: http://jilawww.colorado.edu/jin/

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 86, Iss. 3 — September 2012

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Spatially selective optical pumping with hollow light beams. (a) An image of the horizontal hollow light beam. (b) Illustration of the two intersecting hollow light beams used to optically pump atoms at the edges of the trapped atom cloud. (c) Schematic level diagram showing the optical pumping and imaging transitions. The relevant states at $B = 208.2$ G are labeled with the hyperfine quantum numbers of the $B = 0$ states to which they adiabatically connect.Reuse & Permissions
Figure 2
Measured momentum distribution for a weakly interacting Fermi gas. The momentum distribution of the central 16 $%$ of a harmonically trapped gas is obtained from the average of twelve images. The solid line shows a fit to a homogeneous momentum distribution, where $T$ is fixed to the value obtained from the trap-averaged distribution and $k_{F}$ is the only fit parameter. (Inset) For comparison, we show the trap-averaged distribution, taken from an average of six images, with fits to the expected momentum distribution for an ideal gas in a harmonic trap (dashed line) and to the homogeneous momentum distribution (solid line).Reuse & Permissions
Figure 3
Fit results as a function of the fraction of atoms probed. (a) As the fraction of atoms probed is decreased, the reduced $χ^{2}$ for the fit to a homogeneous gas momentum distribution decreases dramatically and approaches a value of 1.6 for fractions less than $40 %$ . The minimum $χ^{2}$ is limited by systematic noise in the image (i.e., fringes). (b) The best fit value of $k_{F}$ increases as we increasingly probe only the atoms in the central (highest density) part of our trap. A model of the optical pumping by the hollow light beams yields an average local $k_{F}$ indicated by the solid line. As an indication of the density inhomogeneity, the shaded region shows the spread (standard deviation) in $k_{F}$ from the model.Reuse & Permissions
Figure 4
Measured $T / T_{F}$ vs the fraction of atoms probed. Here, we fit the measured momentum distribution to a homogeneous gas distribution with two free parameters, $T / T_{F}$ and $k_{F}$ . The density inhomogeneity of the probed gas results in $T / T_{F}$ that is much larger than expected from the calculated average density of the probed gas (solid line). A sharp Fermi surface, characterized by a small fit $T / T_{F}$ , emerges as the fraction of atoms probed decreases. The dashed line shows the result of fitting to model calculations of the probed momentum distribution, which agrees well with the data.Reuse & Permissions
Figure 5
Modeling the spatially selective optical pumping. We compare the normalized momentum distribution of the central $38 %$ of the atoms to three different models (dotted, solid, and dashed lines; see text). The data (circles) are obtained from an average of four images. We find that the attenuation of the hollow light beams (inset) does not strongly affect the predicted final momentum distribution when probing a small fraction of the gas. (Inset) We take images of the cloud after a short (1.3-ms) expansion and compare data with the horizontal hollow light beam and without any optical pumping in order to measure the fraction of atoms probed (circles) vs $z / z_{F}$ , where $z_{F} = \sqrt{\frac{2 E_{F, trap}}{m {(2 π ν_{z})}^{2}}}$ . For this data, the fraction probed is 71 $%$ . The prediction of our model (solid line), which includes attenuation of the hollow light beam as it propagates through the cloud, agrees well with the data.Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information