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arXiv:cond-mat/0601011 · Physical Review A

Spin noise spectroscopy to probe quantum states of ultracold fermionic atom gases

Bogdan Mihaila, Scott A. Crooker, Krastan B. Blagoev, Dwight G. Rickel, P. B. Littlewood, Darryl Lyle Smith

Published Dec 7, 2006• 15 citations

Abstract

We theoretically demonstrate that optical measurements of electron spin noise can be a spectroscopic probe of the entangled quantum states of ultracold fermionic atom gases and unambiguously reveal the detailed nature of the underlying interatomic correlations. Different models of the effective interatomic interactions predict entirely new sets of resonances in the spin noise spectrum. Once the correct effective interatomic interaction model is identified, the detailed noise line shapes of the spin noise can be used to constrain this model. We estimate the magnitude of spin noise signals expected in ultracold fermionic atom gases via noise measurements in classical alkali vapors, which demonstrate the feasibility of this approach.

DOI: 10.1103/physreva.74.063608

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We theoretically demonstrate that optical measurements of electron spin noise can be a spectroscopic probe of the entangled quantum states of ultracold fermionic atom gases and unambiguously reveal the detailed nature of the underlying interatomic correlations. Different models of the effective interatomic interactions predict entirely new sets of resonances in the spin noise spectrum. Once the correct effective interatomic interaction model is identified, the detailed noise line shapes of the spin noise can be used to constrain this model. We estimate the magnitude of spin noise signals expected in ultracold fermionic atom gases via noise measurements in classical alkali vapors, which demonstrate the feasibility of this approach.

We present a general derivation of the electron spin noise power spectrum in alkali gases as measured by optical Faraday rotation, which applies to both classical gases at high temperatures as well as ultracold quantum gases. We show that the spin-noise power spectrum is determined by an electron spin-spin correlation function, and we find that measurements of the spin-noise power spectra for a classical gas of

^{41}\mathrm{K}

atoms are in good agreement with the predicted values. Experimental and theoretical spin noise spectra are directly and quantitatively compared in both longitudinal and transverse magnetic fields up to the high magnetic-field regime (where Zeeman energies exceed the intrinsic hyperfine energy splitting of the

^{41}\mathrm{K}

ground state).

Recent success in manipulating ultracold atomic systems allows one to probe different strongly correlated regimes in one dimension. Regimes such as the (spin-coherent) Luttinger liquid and the spin-incoherent Luttinger liquid can be realized by tuning the interatomic interaction strength and trap parameters. We identify the noise correlations of density fluctuations as a robust observable (uniquely suitable in the context of trapped atomic gases) to discriminate between these two regimes. Finally, we address the prospects of realizing and probing these phenomena experimentally using optical lattices.

We develop a theory of spin-noise spectroscopy of itinerant, noninteracting, and spin-carrying fermions in different regimes of temperature and disorder. We use kinetic equations for the density matrix in spin variables. We find a general result with a clear physical interpretation, and discuss its dependence on temperature, the size of the system, and applied magnetic field. We consider two classes of experimental probes: (1) electron-spin-resonance-type measurements, in which the probe response to a uniform magnetization increases linearly with the volume sampled and (2) optical Kerr/Faraday rotation-type measurements, in which the probe response to a uniform magnetization increases linearly with the length of the light propagation in the sample but is independent of the cross section of the light beam. Our theory provides a framework for interpreting recent experiments on atomic gases and conduction electrons in semiconductors and provides a baseline for identifying the effects of interactions on spin-noise spectroscopy.

This thesis describes experiments which investigate ultracold atom \nensembles in an optical lattice. Such quantum gases are powerful models for solid state physics. Several novel methods are demonstrated that probe the special properties of strongly correlated states in lattice potentials. Of these, quantum noise spectroscopy reveals spatial correlations in such states, which are hidden when using the usual methods of probing atomic gases. Another spectroscopic technique makes it possible to demonstrate the existence of a shell structure of regions with constant densities. Such coexisting phases separated by sharp boundaries had been theoretically predicted for the Mott insulating state.\nThe tunneling processes in the optical lattice in the strongly correlated regime are probed by preparing the ensemble in an optical superlattice potential. This allows the time-resolved observation of the tunneling dynamics, and makes it possible to directly identify correlated tunneling processes.\n