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Physical Review A

Temporal optical memory based on coherent population and two-photon coherence oscillations

A. Eilam, A. D. Wilson‐Gordon

Published Jul 5, 2018• 6 citations
Publisher

Abstract

We consider the ${F}_{g}=1\ensuremath{\rightarrow}{F}_{e}=1$ transition between the ground and excited hyperfine levels in alkali-metal vapor interacting with $\ensuremath{\sigma}$ linearly polarized control and probe fields whose polarizations can be either parallel or perpendicular to each other. We develop a matrix formulation that allows a solution of the Bloch equations to all orders in the pump and probe Rabi frequencies. Using this formalism, we calculate the steady-state probe absorption spectrum, the coherent population oscillations (CPOs), and two-photon coherence, in the absence (degenerate case) and presence (nondegenerate case) of a longitudinal magnetic field. We then calculate the probe storage when the pump is switched off and on again. We are particularly interested in whether the probe regains its original temporal shape when the pump is switched on again for the case of identical pump and probe frequencies. We show that, in the nondegenerate case, the restored probe does not regain its original shape whereas, in the degenerate case, the original shape is restored. This can be explained by considering the relative magnitudes of the CPOs which do not remember the temporal shape of the probe and the two-photon coherence oscillations which store the probe shape when the pump is switched off, as in electromagnetically induced transparency memories. In the nondegenerate case, the CPOs are much stronger than the two-photon coherence oscillations whereas, in the degenerate case, they are of similar magnitudes. Thus it is the two-photon coherence oscillations that are responsible for the restoration of the temporal shape of the probe in the degenerate case.

DOI
10.1103/physreva.98.013808

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We consider the Fg=1\ensuremath→Fe=1{F}_{g}=1\ensuremath{\rightarrow}{F}_{e}=1Fg​=1\ensuremath→Fe​=1 transition between the ground and excited hyperfine levels in alkali-metal vapor interacting with \ensuremathσ\ensuremath{\sigma}\ensuremathσ linearly polarized control and probe fields whose polarizations can be either parallel or perpendicular to each other. We develop a matrix formulation that allows a solution of the Bloch equations to all orders in the pump and probe Rabi frequencies. Using this formalism, we calculate the steady-state probe absorption spectrum, the coherent population oscillations (CPOs), and two-photon coherence, in the absence (degenerate case) and presence (nondegenerate case) of a longitudinal magnetic field. We then calculate the probe storage when the pump is switched off and on again. We are particularly interested in whether the probe regains its original temporal shape when the pump is switched on again for the case of identical pump and probe frequencies. We show that, in the nondegenerate case, the restored probe does not regain its original shape whereas, in the degenerate case, the original shape is restored. This can be explained by considering the relative magnitudes of the CPOs which do not remember the temporal shape of the probe and the two-photon coherence oscillations which store the probe shape when the pump is switched off, as in electromagnetically induced transparency memories. In the nondegenerate case, the CPOs are much stronger than the two-photon coherence oscillations whereas, in the degenerate case, they are of similar magnitudes. Thus it is the two-photon coherence oscillations that are responsible for the restoration of the temporal shape of the probe in the degenerate case.
We review our previous work on pump-probe spectroscopy in realistic degenerate two-level systems and model systems. In particular, we discuss the role of transfer of coherence (TOC) between the ground and excited hyperfine states in producing electromagnetically-induced transparency (EIA) peaks in the probe spectrum, when an Fg goes to Fe = Fg +1 transition in an alkali-metal atom interacts with a strong pump and weak probe that have perpendicular polarizations. When the pump is rho+ polarized and the probe pi polarized, this system can be modelled by an N system. We also discuss the role of transfer of population (TOP) between the Zeeman levels of the ground hyperfine state in producing EIA peaks when the pump and probe have the same polarization. This system can be modelled using a double two-level system. The role of Doppler broadening and phase-changing collisions in modifying the EIA-TOC and EIA-TOP absorption and refraction spectra is also discussed. All these spectra were calculated using MATLAB programs that both construct and solve the relevant Bloch equations. In our recent work, we consider the effect of a strong probe on the pump absorption and refraction spectra when the pump and probe polarizations are linear and perpendicular. It is difficult to solve this problem numerically due to the large number frequencies involved. In order to simplify the problem, we considered two cases: (i) rho+ polarized pump and pi polarized probe, and (ii) rho+ polarized pump and rho- polarized probe, and investigated a series of transitions in both Rb and Cs, using modified versions of the MATLAB programs devised for the weakprobe case. A number of interesting differences from the weak-probe case were found. For example, when the probe is sufficiently strong, we found the pump and probe spectra to show complementary behavior. In addition, as the number of Zeeman levels increase, the EIA peaks become progressively sharper, and are accompanied by steeper dispersion.
We study the pump and probe absorption spectra, as a function of the probe detuning, in a degenerate two-level atomic system, for the case where the probe intensity is high enough to affect the pump absorption. The theory is valid for any ${F}_{g}\ensuremath{\rightarrow}{F}_{e}$ alkali-metal transition interacting with an arbitrarily intense pump and probe (with general Rabi frequencies ${\ensuremath{\Omega}}_{1,2}$) which are perpendicularly polarized with either ${\ensuremath{\sigma}}_{\ifmmode\pm\else\textpm\fi{}}$ or $\ensuremath{\pi}$ polarization. We have constructed a computer program that can calculate the spectra without requiring one to write out the Bloch equations explicitly. We show that, when the pump is ${\ensuremath{\sigma}}_{\ifmmode\pm\else\textpm\fi{}}$ polarized and the probe $\ensuremath{\pi}$ polarized, or vice versa, the pump and probe absorptions depend on the Zeeman coherences between the nearest-neighboring ground or excited Zeeman sublevels, whereas when the pump is ${\ensuremath{\sigma}}_{+}$ polarized and the probe ${\ensuremath{\sigma}}_{\ensuremath{-}}$ polarized, or vice versa, the Zeeman coherences that directly determine the absorption are between next-nearest neighbors. We report calculations of the pump and probe absorption spectra for the cycling ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition in the D2{D}_{2}D2​ line of 87Rb^{87}\text{R}\text{b}87Rb, interacting with a resonant ${\ensuremath{\sigma}}_{+}$-polarized pump and either a $\ensuremath{\pi}$- or a ${\ensuremath{\sigma}}_{\ensuremath{-}}$- polarized probe. The probe and pump absorption spectra are analyzed by considering the contributions that derive from the individual ${m}_{g}\ensuremath{\rightarrow}{m}_{e}$ transitions. We then show how these contributions depend on the ground- and excited-state populations and Zeeman coherences, and investigate the role played by transfer of coherence from the excited to the ground hyperfine state. We show that the pump and probe absorption spectra are mirror images of each other when ${\ensuremath{\Omega}}_{1}\ensuremath{\ge}{\ensuremath{\Omega}}_{2}>\ensuremath{\Gamma}$, and have the same behavior at line center and complementary behavior in the wings, when ${\ensuremath{\Omega}}_{1}\ensuremath{\ge}{\ensuremath{\Omega}}_{2}<\ensuremath{\Gamma}$ ($\ensuremath{\Gamma}$ is the rate of spontaneous decay from Fe{F}_{e}Fe​ to Fg{F}_{g}Fg​).
For a transition ${F}_{e}=0\ensuremath{\leftrightarrow}{F}_{g}=1$ driven by a linearly polarized light and probed by a transverse light, which has two equal circular components and is orthogonal to the linear polarization of the drive field and magnetic field, quantum coherence effects are investigated. Due to the coupling between the drive Rabi frequency and the Zeeman splitting, electromagnetically induced transparency, electromagnetically induced absorption, and the transition from positive to negative dispersion are obtained, as well as the populations coherently oscillating with a pump-probe detuning in the steady state. At the zero pump-probe detuning, the subluminal and superluminal light propagations are predicted. Finally, there exist the large population fluctuations when we vary the pump-probe detuning.
We show that a system characterized by long-lived coherent population oscillations (CPOs), such as a two-level system that decays via a shelving state, can be used to construct a spatial optical memory. In the presence of a cw control field, a field is generated at the four-wave mixing (FWM) frequency with the same spatial profile as the initial probe. When the control field is switched off, these spatial profiles are encoded in the CPOs of the ground and storage states. When the control field is switched on again, the probe and FWM fields are retrieved simultaneously with the same spatial profiles as the initial probe.
Coherent optical memory based on electromagnetically induced transparency (EIT) offers a convenient way to convert the frequency or polarization of an optical probe pulse by storing in one $\mathrm{\ensuremath{\Lambda}}$ system and retrieving in another $\mathrm{\ensuremath{\Lambda}}$ system. We present a theoretical study on the efficiency variation of such an EIT-memory-based optical converter in an atomic system with degenerate Zeeman states. Based on the Maxwell-Bloch equation, we obtain an approximate analytic solution for the converted light pulses which clarifies that two major factors affect the efficiency of the converted pulses. The first one is the finite bandwidth effect of the pulses and the difference in the delay-bandwidth product of the writing and reading channel due to the difference in the transition dipole moment. The second one is the mismatch between the stored ground-state coherence and the ratio of the Clebsch-Gordan coefficients for the probe and control transition in the reading channel, which results in a nonadiabatic energy loss. To correspond to real experimental conditions, we also perform a numerical calculation of the variation in conversion efficiency versus the Zeeman population distribution under the Zeeman-state optical pumping in storing a ${\ensuremath{\sigma}}^{+}$-polarized pulse and retrieving with ${\ensuremath{\sigma}}^{\ensuremath{-}}$ polarization in cesium atoms. Our work provides essential physical insights and quantitative knowledge for the development of a coherent optical converter based on EIT-memory.
We report on the storage of light via the phenomenon of coherent population oscillation (CPO) in an atomic cesium vapor at room temperature. In the experiment the optical information of a probe field is stored in the CPO of two ground states of a $\ensuremath{\Lambda}$ three-level system formed by the Zeeman sublevels of the hyperfine transition $F=3\ensuremath{\rightarrow}{F}^{\ensuremath{'}}=2$ of the cesium D2{D}_{2}D2​ line. We show directly that this CPO-based memory is very insensitive to stray magnetic field inhomogeneities and presents a lifetime which is limited mainly by atomic motion. A theoretical simulation of the measured spectra was also developed and is in very good agreement with the experiment.