[Paper Review] Single-particle versus many-body phase coherence in an interacting Fermi gas

Giovanni Pecci, Piero Naldesi+2 more|arXiv (Cornell University)|May 21, 2021

Cold Atom Physics and Bose-Einstein Condensates4 citations

TL;DR

This paper demonstrates a time-resolved interferometric protocol to distinguish single-particle phase coherence from many-body quantum coherence in an interacting degenerate Fermi gas. By releasing the gas from a ring-shaped trap with an effective magnetic flux, it shows that single-particle coherence manifests as spiral interference patterns at intermediate times, while many-body coherence—evidenced by off-diagonal long-range order—emerges as stepwise modulations in density-density correlations at long times.

ABSTRACT

In quantum mechanics, each particle is described by a complex valued wave-function characterized by amplitude and phase. When many particles interact each other, cooperative phenomena give rise to a quantum many-body state with a specific quantum coherence. What is the interplay between single-particle's phase coherence and many-body quantum coherence? Over the years, such question has been object of profound analysis in quantum physics. Here, we demonstrate how the time-dependent interference formed by releasing an interacting degenerate Fermi gas from a specific matter-wave circuit in an effective magnetic field can tell apart the two notions. Single-particle phase coherence, indicated by the first-order correlator, and many-body quantum coherence, indicated by the density-density correlator, are displayed as distinct features of the interferogram. Single particle phase coherence produces spiral interference of the Fermi orbitals at intermediate times. Many-body quantum coherence emerges as long times interference. The interplay between single-particle coherence and many-body coherence is reflected in a stepwise dependence of the interference pattern on the effective magnetic field.

Motivation & Objective

• To disentangle single-particle phase coherence from many-body quantum coherence in interacting Fermi systems.
• To investigate how interactions affect the emergence and visibility of interference features linked to these two coherence types.
• To establish a single experimental protocol capable of probing both coherence mechanisms in a controlled, time-evolving setup.
• To link the stepwise dependence of long-time interference patterns on effective magnetic flux to the presence of off-diagonal long-range order (ODLRO).

Proposed method

• Use a time-of-flight expansion protocol in a ring-shaped trap with an effective magnetic flux to induce persistent currents and interfere with a central Fermi gas.
• Track the time evolution of the system’s density and pair correlation functions to extract single-particle and many-body coherence signatures.
• Analyze the first-order correlation function (G1) to identify single-particle coherence via spiral interference patterns at intermediate times.
• Examine the second-order density-density correlator (G2) to detect many-body coherence, particularly off-diagonal long-range order (ODLRO), at long times.
• Define a visibility metric for momentum-space correlations along the anti-diagonal (k, -k) to quantify ODLRO, independent of system size N.
• Use lattice discretization of the two-body density matrix and natural orbitals to compute the scaling of the largest eigenvalue λ₀(N) as a measure of ODLRO strength.

Experimental results

Research questions

• RQ1 How do single-particle phase coherence and many-body quantum coherence manifest differently in the time evolution of an interacting Fermi gas?
• RQ2 What is the role of interaction strength in blurring the dislocations associated with single-particle orbital interference?
• RQ3 How does the long-time density-density correlation respond to changes in effective magnetic flux, and what does this reveal about many-body coherence?
• RQ4 Can the visibility of momentum-space correlations along the anti-diagonal (k, -k) serve as a robust, system-size-independent indicator of ODLRO in fermionic systems?
• RQ5 To what extent do the interference patterns at intermediate and long times reflect distinct quantum coherence mechanisms in a Fermi gas?

Key findings

• Single-particle phase coherence produces spiral interference patterns in the time-of-flight images at intermediate times, directly linked to the Fermi surface and orbital interference.
• Many-body quantum coherence, characterized by off-diagonal long-range order (ODLRO), emerges as a stepwise modulation in the long-time density-density correlation function as a function of effective magnetic flux.
• The visibility of the momentum-space correlation function along the anti-diagonal (k, -k) is independent of system size N, providing a robust, universal indicator of ODLRO.
• Increasing interaction strength leads to a progressive blurring of the dislocations in the interferogram, indicating a breakdown of the independent-particle picture.
• The long-time behavior of the density-density correlator is directly related to momentum-space correlations via the time-of-flight mapping, with the connected part capturing ODLRO information.
• The scaling of the largest eigenvalue of the two-body density matrix, λ₀(N), follows O(N^α) with 0 < α < 1 in the presence of quasi-ODLRO, indicating reduced but still macroscopic coherence.