ACQAO

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Does distance make the heart grow fonder?

19 April 2008

Andrew Sykes

Strongly correlated, many-body quantum systems present one of the major theoretical challenges to physicists. Understanding these systems can lead to major advances in new technologies as well as increasing our fundamental understanding of the world around us. Theorists Andrew Sykes, Matt Davis and Karen Kheruntsyan of the University of Queensland alongside Dimitri Gangardt from the University of Birmingham have taken up this challenge, and succeeded in generating a finite temperature phase diagram of the second-order correlation function, in a system of interacting bosons confined to move in one spatial dimension. The one-dimensional (1D) Bose gas is perhaps the simplest paradigm we have of a strongly correlated quantum gas, hence understanding the correlations of this system in different regimes carries significant general interest.

By disecting the “interaction strength versus temperature” phase diagram up into six separate regimes, and identifying the dominating physics in each, analytic expressions were derived for the second order spatial correlation function g(2)(r). Given a particle at a certain location, this so-called pair correlation ascribes a probability of finding a second particle at a distance r from the first. It is a direct consequence of the quantum field-like behaviour of particles. This work extends our knowledge of these systems beyond simple density profiles.

The complex interplay between thermal effects versus interaction-induced behaviour revealed an intriguing "cycle" of correlations. This "cycle" (displayed in Fig. 1) shows the fermionic-like behaviour at strong interaction, the quasi-condensate behaviour at weak interaction and cold temperatures and the decoherent gases at high temperatures, as well as shedding light on the transitions between different regimes.

Dimitri Gangardt

The existence of such a rich amount of physics in this system has not escaped the attention of experimentalists in the field. Professor Mark Raizen from the University of Texas, in Austin has proposed a method of spatially resolved single atom counting which could be employed to measure these correlations. The measurements would need to be performed in-situ, that is the atoms would not be released from the trap when the measurement occurs. Although the measurements have not been done yet, Raizen is confident that the technique he proposes could obtain the spatial resolution required to observe the behaviour predicted by theorists.

Temperature (τ) versus interaction strength (γ) phase diagram showing six distinct physical regimes of the interacting 1D Bose gas problem, together with the characteristic behavior of the pair correlation function g⁽²⁾(r) as a function of the distance r. The temperature τ is in units of the temperature of quantum degeneracy T_d. On each graph we show the characteristic correlation length, which is given by one of the following typical length scales: the thermal de Broglie wavelength Λ_T, the mean interparticle separation 1/n (where n is the 1D linear density), the healing length ξ, or the phase coherence length l_φ.

To read more about this see the article A. G. Sykes, D. M. Gangardt, M. J. Davis, K. Viering, M. G. Raizen, and K. V. Kheruntsyan, Phys. Rev. Lett. 100, 160406 (2008), entitled "Spatial nonlocal pair correlations in a repulsive 1D Bose gas".

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For further information, contact: Mr Andrew Sykes, email sykes@physics.uq.edu.au, Dr Matt Davis, email mdavis@physics.uq.edu.au, or Dr Karen Kheruntsyan, email karen.kheruntsyan@uq.edu.au, ARC Centre of Excellence for Quantum-Atom Optics, School of Physical Sciences, The University of Queensland.