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arXiv:0905.3251 · Physical Review Letters

Pump-Probe Spectroscopy of Two-Body Correlations in Ultracold Gases

Christiane P. Koch, Ronnie Kosloff

Published Dec 21, 2009• 10 citations
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Abstract

We suggest pump-probe spectroscopy to study pair correlations that determine the many-body dynamics in weakly interacting, dilute ultracold gases. A suitably chosen, short laser pulse depletes the pair density locally, creating a "hole" in the electronic ground state. The dynamics of this nonstationary pair density is monitored by a time-delayed probe pulse. The resulting transient signal allows us to spectrally decompose the hole and to map out the pair correlation function.

DOI
10.1103/physrevlett.103.260401

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We suggest pump-probe spectroscopy to study pair correlations that determine the many-body dynamics in weakly interacting, dilute ultracold gases. A suitably chosen, short laser pulse depletes the pair density locally, creating a "hole" in the electronic ground state. The dynamics of this nonstationary pair density is monitored by a time-delayed probe pulse. The resulting transient signal allows us to spectrally decompose the hole and to map out the pair correlation function.
Two atoms in an ultracold gas are correlated at short interatomic distances due to threshold effects in which the potential energy of their interaction dominates the kinetic energy. The correlations manifest themselves in a distinct nodal structure of the density matrix at short interatomic distances. Pump-probe spectroscopy has recently been suggested [Phys. Rev. Lett. 103, 260401 (2009)] to probe these pair correlations: A suitably chosen, short photoassociation laser pulse depletes the ground-state pair density within the photoassociation window, creating a nonstationary wave packet in the electronic ground state. The dynamics of this nonstationary wave packet is monitored by time-delayed probe and ionization pulses. Here we discuss how the choice of the pulse parameters affects the experimental feasibility of this pump-probe spectroscopy of two-body correlations.
Ultrashort nonresonant electromagnetic pulses applied to effective one-electron systems may operate on the electronic state as a position or momentum translation operator. As derived here, extension to many-body correlated systems exposes qualitatively new aspects. For instance, to the lowest order in the electric field intensity the action of the pulse is expressible in terms of the two-body reduced density matrix enabling us to probe various facets of electronic correlations. As an experimental realization we propose a pump-probe scheme in which after a weak, swift ``kick'' by the nonresonant pulse the survival probability for remaining in the initial state is measured. This probability we correlate to the two-body reduced density matrix. Since the strength of electronic correlation is bond-length sensitive, measuring the survival probability may allow for a direct insight into the bond-dependent two-body correlation in the ground state. As an illustration, full numerical calculations for two molecular systems are provided and different measures of electronic correlations are analyzed.
The dependence of the electronic absorption spectrum of a dye molecule on the time of delay between the excitation of the molecule by a pump-laser pulse and the probing of the absorption by a test-laser pulse is studied. The effect of dephasing of the molecular transition arising from the interaction with dissipative systems is described by a stochastic modulation of the electronic transition frequency. It is shown that in the case when the two laser pulses are short compared with the correlation time of the frequency modulation and when the spectral linewidth of the pump-laser light is smaller than the bandwidth of the equilibrium absorption spectrum, hole burning appears although the molecules have equal mean transition frequencies. This effect arises from non-Markovian correlations between the dephasings of the molecule during the actions of the pump- and the test-laser pulse. With increasing delay time the holes are smoothed out and disappear when the delay time exceeds the correlation time. Such effects were found in recent femtosecond absorption experiments by Shank et al. [in Ultrafast Phenomena V, dited by G. R. Fleming and A. E. Siegman (Springer, Berlin, 1986), p. 179].
Ultrafast pump-probe spectroscopy with high temporal and spectral resolutions provides new insight into ultrafast nonequilibrium phenomena. We propose that transient interference between pump and probe pulses is realized in pump-probe spectroscopy of band and Mott insulators, which can be observed only after recent developments of ultrafast spectroscopic techniques. A continuum structure in the excitation spectrum of band insulators is found to act as a medium for storing the spectral information of the pump pulse, and the spectrum detected by the probe pulse is interfered with by the medium, generating the transient interference in the energy domain. We also demonstrate the transient interference in the presence of electron correlations in a one-dimensional half-filled Hubbard model. Furthermore, bosons coupled to electrons additively contribute to the interference. Our finding will provide an interpretation of probe-energy-dependent oscillations recently observed in the pump-probe spectrum for a two-dimensional Mott insulator.
We show that entangled photons may be used in coherent multidimensional nonlinear spectroscopy to provide information on matter by scanning photon wave function parameters (entanglement time and delay of twin photons), rather than frequencies and time delays, as is commonly done with classical pulses. Signals are expressed and interpreted intuitively in terms of products of matter and field correlation functions using a diagrammatic close time path loop formalism which reveals the entangled quantum pathways of the fields and matter. The pump-probe signal measured when the pump and the probe are in a twin entangled state shows two-photon resonant contributions which scale linearly rather than quadratically with the incident beam intensity and reveal frequencies of off-resonant transitions. Two-dimensional spectrograms obtained by double Fourier transform of the signal with respect to the entanglement time and delay of the twins could provide detailed information on correlations among states and dynamical processes with high temporal resolution. The analogy with multidimensional time-domain optical techniques which use sequences of short classical pulses and pulse shaping algorithms is pointed out.