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Title: Detecting Correlation Functions of Ultracold Atoms through Fourier Sampling of Time-of-Flight Images

Abstract

We propose a detection method for ultracold atoms which allows reconstruction of the full one-particle and two-particle correlation functions from the measurements. The method is based on Fourier sampling of the time-of-flight images through two consecutive impulsive Raman pulses. For applications of this method, we discuss a few examples, including detection of phase separation between superfluid and Mott insulators, various types of spin or superfluid orders, entanglement, exotic or fluctuating orders.

Authors:
 [1]
  1. FOCUS Center and MCTP, Department of Physics, University of Michigan, Ann Arbor, Michigan 48109 (United States)
Publication Date:
OSTI Identifier:
20778801
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 96; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevLett.96.103201; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATOMS; CORRELATION FUNCTIONS; FOURIER ANALYSIS; IMAGES; RAMAN SPECTRA; SAMPLING; SPIN; SUPERFLUIDITY; TIME-OF-FLIGHT METHOD

Citation Formats

Duan, L.-M. Detecting Correlation Functions of Ultracold Atoms through Fourier Sampling of Time-of-Flight Images. United States: N. p., 2006. Web. doi:10.1103/PHYSREVLETT.96.1.
Duan, L.-M. Detecting Correlation Functions of Ultracold Atoms through Fourier Sampling of Time-of-Flight Images. United States. doi:10.1103/PHYSREVLETT.96.1.
Duan, L.-M. Fri . "Detecting Correlation Functions of Ultracold Atoms through Fourier Sampling of Time-of-Flight Images". United States. doi:10.1103/PHYSREVLETT.96.1.
@article{osti_20778801,
title = {Detecting Correlation Functions of Ultracold Atoms through Fourier Sampling of Time-of-Flight Images},
author = {Duan, L.-M.},
abstractNote = {We propose a detection method for ultracold atoms which allows reconstruction of the full one-particle and two-particle correlation functions from the measurements. The method is based on Fourier sampling of the time-of-flight images through two consecutive impulsive Raman pulses. For applications of this method, we discuss a few examples, including detection of phase separation between superfluid and Mott insulators, various types of spin or superfluid orders, entanglement, exotic or fluctuating orders.},
doi = {10.1103/PHYSREVLETT.96.1},
journal = {Physical Review Letters},
number = 10,
volume = 96,
place = {United States},
year = {Fri Mar 17 00:00:00 EST 2006},
month = {Fri Mar 17 00:00:00 EST 2006}
}
  • We propose to utilize density distributions from a series of time-of-flight images of an expanding cloud to reconstruct single-particle correlation functions of trapped ultracold atoms. In particular, we show how this technique can be used to detect off-diagonal correlations of atoms in a quasi-one-dimensional trap, where both real- and momentum-space correlations are extracted at a quantitative level. The feasibility of this method is analyzed with specific examples, taking into account finite temporal and spatial resolutions in experiments.
  • This paper develops techniques to evaluate the discrete Fourier transform (DFT), the autocorrelation function (ACF), and the cross-correlation function (CCF) of time series which are not evenly sampled. The series may consist of quantized point data (e.g., yes/no processes such as photon arrival). The DFT, which can be inverted to recover the original data and the sampling, is used to compute correlation functions by means of a procedure which is effectively, but not explicitly, an interpolation. The CCF can be computed for two time series not even sampled at the same set of times. Techniques for removing the distortion ofmore » the correlation functions caused by the sampling, determining the value of a constant component to the data, and treating unequally weighted data are also discussed. FORTRAN code for the Fourier transform algorithm and numerical examples of the techniques are given. 20 refs.« less
  • Reversible ischemia in myocardial segments with severe hypoperfusion ({le}50% of normal activity) on stress Tc-99m-Sestamibi (MIBI) images was assessed with ECG-gated tomographic (GSPECT) indices of myocardial thickening, as reflected by an increase in regional count density during systole. GSPECT bullseye plots were generated for each of 8 frames acquired after stress MIBI injection in 39 patients with coronary artery disease and at least one severe perfusion defect on summed SPECT images. Using first harmonic Fourier amplitude (AMP) and AMP to perfusion ratio (APR) images, regional myocardial systolic thickening was assessed using a 5-segment model, scored 0 to 3, for absent,more » minimal, mildly reduced or normal thickening. These data were regionally compared with defect reversibility assessed using a separate-day or a preceding same-day resting MIBI injection images, in which these segments were scored from 0 to 3 for absent, minimal, partial or complete defect reversibility. Of 91 severe stress defects, 16 showed absent, 18 minimal, 43 partial, and 14 complete reversibility on resting images. Both AMP and APR scores were in statistically significant agreement (p=.0218 and .0006) with resting image reversibility grades, with 79% (p=.0324) and 86% (p=.0001) agreement on the presence of reversibility on resting imaging, respectively. AMP correctly identified 89% of the reversibility defects on rest images, while the APR identified 99% (p=.0248 vs. AMP). On analysis of segment scores, the AMP slightly underestimated the degree of rest image reversibility (p=.0235), while APR images indicated more reversibility thin did resting images (p=.0092). In conclusion, GSPECT MIBI bullseye Fourier AMP images correlate well with the pattern of reversibility on resting MIBI in severe stress perfusion defects. When indexed for the degree of hypoperfusion, the Fourier images depict a greater degree of defect reversibility than resting MIBI images.« less