Thermal blurring of a coherent Fermi gas

Abstract

It is generally assumed that a condensate of paired fermions at equilibrium is characterized by a macroscopic wavefunction with a well-defined, immutable phase. In reality, all systems have a finite size and are prepared at non-zero temperature; the condensate has then a finite coherence time, even when the system is isolated in its evolution and the particle number $N$ is fixed. The loss of phase memory is due to interactions of the condensate with the excited modes that constitute a dephasing environment. This fundamental effect, crucial for applications using the condensate of pairs' macroscopic coherence, was scarcely studied. We link the coherence time to the condensate phase dynamics, and we show with a microscopic theory that the time derivative of the condensate phase operator $\hat{\theta }\_0$ is proportional to a chemical potential operator that we construct including both the pair-breaking and pair-motion excitation branches. In a single realization of energy $E$, $\hat{\theta }\_0$ evolves at long times as $-2\mu \_\mathrm{mc}(E)t/\hslash$ where $\mu \_\mathrm{mc}(E)$ is the microcanonical chemical potential; energy fluctuations from one realization to the other then lead to a ballistic spreading of the phase and to a Gaussian decay of the temporal coherence function with a characteristic time $\propto N^{1/2}$. In the absence of energy fluctuations, the coherence time scales as $N$ due to the diffusive motion of $\hat{\theta }\_0$. We propose a method to measure the coherence time with ultracold atoms, which we predict to be tens of milliseconds for the canonical ensemble unitary Fermi gas.

published version in English (13 pages) and in French (14 pages)

References in corpus (14)

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Cited by in corpus (14)

• Boundary time crystals
• Three-phonon and four-phonon interaction processes in a pair-condensed Fermi gas
• Cumulant theory of the unitary Bose gas: Prethermal and Efimovian dynamics
• Spin-squeezed states for metrology
• Absorption and emission of a collective excitation by a fermionic quasiparticle in a Fermi superfluid
• The temporal coherence of a photon condensate: A quantum trajectory description
• Algebraic Time Crystallization in a Two-dimensional Superfluid
• Landau-Khalatnikov phonon damping in strongly interacting Fermi gases
• Space- and time-crystallization effects in multicomponent superfluids
• Phonon damping in a 2D superfluid: insufficiency of Fermi's golden rule at low temperature
• Coherence time of a Bose-Einstein condensate in an isolated harmonically trapped gas
• Damping of elementary excitations in one-dimensional dipolar Bose gases
• Random walk of a massive quasiparticle in the phonon gas of an ultralow temperature superfluid
• Phase spreading and temporal coherence of a pair-condensed Fermi gas at low temperature