Suppression of Density Fluctuations in a Quantum Degenerate Fermi Gas

Abstract

We study density profiles of an ideal Fermi gas and observe Pauli suppression of density fluctuations (atom shot noise) for cold clouds deep in the quantum degenerate regime. Strong suppression is observed for probe volumes containing more than 10,000 atoms. Measuring the level of suppression provides sensitive thermometry at low temperatures. After this method of sensitive noise measurements has been validated with an ideal Fermi gas, it can now be applied to characterize phase transitions in strongly correlated many-body systems.PACS numbers: 03.75. Ss, 05.30.Fk, 67.85.Lm Systems of fermions obey the Pauli exclusion principle. Processes that would require two fermions to occupy the same quantum state are suppressed. In recent years, several classic experiments have directly observed manifestations of Pauli suppression in Fermi gases. Antibunching and the suppression of noise correlations are a direct consequence of the forbidden double occupancy of a quantum state. Such experiments were carried out for electrons [1][2][3], neutral atoms [4,5], and neutrons [6]. In principle, such experiments can be done with fermions at any temperature, but in practice low temperatures increase the signal. A second class of (two-body) Pauli suppression effects, the suppression of collisions, requires a temperature low enough such that the de Broglie wavelength of the fermions becomes larger than the range of the interatomic potential and p-wave collisions freeze out. Experiments observed the suppression of elastic collisions [7,8] and of clock shifts in radio frequency spectroscopy [9,10].Here we report on the observation of Pauli suppression of density fluctuations, a many-body phenomenon which occurs only at even lower temperatures in the quantum degenerate regime, where the Fermi gas is cooled below the Fermi temperature and the low lying quantum states are occupied with probabilities close to one. In contrast, an ideal Bose gas close to quantum degeneracy shows enhanced density fluctuations [11].The development of a technique to sensitively measure density fluctuations was motivated by the connection between density fluctuations and compressibility through the fluctuation dissipation theorem. In this paper, we validate our technique for determining the compressibility by applying it to the ideal Fermi gas. In future work, it could be extended to interesting many-body phases in optical lattices which are distinguished by their incompressibility [12]. These include the band insulator, Mott insulator, and also the antiferromagnet for which spin fluctuations, i.e. fluctuations of the difference in density between the two spin states, are suppressed.Until now, sub-Poissonian number fluctuations of ultracold atoms have been observed only for small clouds of bosons with typically a few hundred atoms [13][14][15][16] and directly [17,18] or indirectly [19] for the bosonic Mott in-

Virial expansion for a strongly correlated Fermi gas with imbalanced spin populations

“…This seems to be now accessible, since the shot noise measurements of the density fluctuations in a weakly interacting Fermi gas have already been demonstrated very recently [36,37]. We find that the spin susceptibility of an attractive Fermi gas at unitarity is strongly suppressed with respect to the ideal Fermi gas result, even well above the degenerate temperature T F .…”

Isothermal-sweep theorems for ultracold quantum gases in a canonical ensemble

“…Although this was proposed as early as in 2005 [23], it has recently been possible to extract this information for two-component Fermi gases, by measuring the density fluctuations and atomic compressibility [24,25]. Combining Eq.…”

“…(26) can be used to extract the temperarure dependence of C, given that κ T can be extracted from the fluctuation-dissipation theorem [24,25]. Having derived the IST for the free, average and trapping energies, and for the entropy, specific heat, pressure and atomic compressibility in a canonical ensemble, next we derive the Virial theorem.…”

Measuring the equation of state of trapped ultracold bosonic systems in an optical lattice within situdensity imaging

“…[20] and Ref. [21] suggested that the FD theorem is an absolute thermometer in an harmonic trap without lattice, through careful normalization [20] of R ∞ (ρ), However, for the small number O(10 5 ) − O(10 6 ) of fermions in their experiments, the estimated temperature deviated from the time-of-flight (TOF) measurements by about 30% [21].…”

“…With this it is possible to determine temperature in the lattice system using the fluctuation-dissipation theorem without invoking theory [19][20][21]. Also the equation of state and the chemical potential can be extracted from the edges using high temperature series expansions, provided those regions are large enough.…”