Probing the Degree of Coherence through the Full 1D to 3D crossover

TL;DR

This study experimentally explores the transition of a quantum degenerate gas of rubidium atoms from a 1D to a 3D regime, revealing how phase fluctuations depend on chemical potential and temperature during the dimensional crossover.

Contribution

It provides a detailed experimental investigation of the full 1D to 3D crossover in a quantum gas, demonstrating how phase fluctuations evolve and are governed by chemical potential and temperature.

Findings

Fluctuations depend on chemical potential and temperature.

Inside the crossover, temperature dependence diminishes as the system becomes 3D.

Fluctuations are governed by occupation of 1D axial collective excitations.

Abstract

We experimentally study a gas of quantum degenerate $^{87}$Rb atoms throughout the full dimensional crossover, from a one-dimensional (1D) system exhibiting phase fluctuations consistent with 1D theory to a three-dimensional (3D) phase-coherent system, thereby smoothly interpolating between these distinct, well-understood regimes. Using a hybrid trapping architecture combining an atom chip with a printed circuit board, we continuously adjust the system's dimensionality over a wide range while measuring the phase fluctuations through the power spectrum of density ripples in time-of-flight expansion. Our measurements confirm that the chemical potential $\mu$ controls the departure of the system from 3D and that the fluctuations are dependent on both $\mu$ and the temperature $T$. Through a rigorous study we quantitatively observe how inside the crossover the dependence on $T$ gradually disappears as the system becomes 3D. Throughout the entire crossover the fluctuations are shown to be determined by the relative occupation of 1D axial collective excitations.