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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Nonclassical polarization properties of two-photon time-delay interference in three-level phase memory media

S. A. Moiseev, M. I. Noskov

Published Feb 25, 1999• 0 citations
Publisher

Abstract

Currently, it is obvious [1] that nonstationary tasks of quantum mechanics in more degree differ from those of classical physics than stationary ones. Accordingly, time- domain quantum optics experiments are very important for deepening our knowledge of quantum dynamics. It appears that a single-photon wave (SPW-) packets [2] are the best objects of quantum optics for investigation of the quantum dynamics at macroscopic level. One of the fundamental problems herein is the comprehension of interactions of quantum fields (SPW4MIN and TPW-packets) with macroscopic media. In particular, this is immediately associated with development of our knowledge about the fundamental properties of the irreversibility and of detecting quantum fields. At present, our notion about interaction of quantum fields with a detector, is mainly based on the phenomenological approaches to the properties of the detector [3]. That is why more exact quantum models of macroscopic detectors must be investigated. One of the macroscopic objects, which can be interesting for these purposes is the resonant quantum (Two-,Three-level) medium with phase memory intensively studied in coherent optics. Unusual properties of quantum time-domain interference effects and of photon echoes initiated in resonant media by interactions with an SPW-packet, have been predicted in our works 4LB4-6]. In the present paper study of the quantum dynamics at interaction of the field with the medium we will carry out by investigation of the two photon echo properties. At that, we consider interaction of a three- level (TL-) medium with polarized two-photon wave packets for the purpose of eliciting new nonclassical polarization properties in quantum dynamics of the echo signals.

DOI
10.1117/12.340108

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Currently, it is obvious [1] that nonstationary tasks of quantum mechanics in more degree differ from those of classical physics than stationary ones. Accordingly, time- domain quantum optics experiments are very important for deepening our knowledge of quantum dynamics. It appears that a single-photon wave (SPW-) packets [2] are the best objects of quantum optics for investigation of the quantum dynamics at macroscopic level. One of the fundamental problems herein is the comprehension of interactions of quantum fields (SPW4MIN and TPW-packets) with macroscopic media. In particular, this is immediately associated with development of our knowledge about the fundamental properties of the irreversibility and of detecting quantum fields. At present, our notion about interaction of quantum fields with a detector, is mainly based on the phenomenological approaches to the properties of the detector [3]. That is why more exact quantum models of macroscopic detectors must be investigated. One of the macroscopic objects, which can be interesting for these purposes is the resonant quantum (Two-,Three-level) medium with phase memory intensively studied in coherent optics. Unusual properties of quantum time-domain interference effects and of photon echoes initiated in resonant media by interactions with an SPW-packet, have been predicted in our works 4LB4-6]. In the present paper study of the quantum dynamics at interaction of the field with the medium we will carry out by investigation of the two photon echo properties. At that, we consider interaction of a three- level (TL-) medium with polarized two-photon wave packets for the purpose of eliciting new nonclassical polarization properties in quantum dynamics of the echo signals.
A new type of three-level photon echo has been predicted and analytically described. In contrast to the conventional three-level echo, whose formation involves three resonant ultrashort excitation pulses spaced in time, two of which are resonant to different optically allowed and adjacent transitions with different frequencies, the echo predicted arises under the conditions of formation of the conventional two-pulse echo and requires only two pump pulses of the same frequency. A theory is developed for the conditions of experiments on generation of a superradiance pulse at the 3 P 0-3 H 6 transition in impurity praseodymium ions in the LaF3 matrix upon ultrashort coherent excitation of the adjacent optically allowed 3 H 4-3 P 0 transition in praseodymium. It is shown that the superradiance pulse after its deexcitation does not polarize the medium at the 3 P 0-3 H 6 generation transition and completely eliminates polarization at the 3 H 4-3 P 0 excitation transition. However, simultaneously, the superradiance pulse transfers the optical coherence from the excitation transition to the optically forbidden 3 H 6-3 H 4 transition. Thus, the phase memory about the effect of the excitation superradiance pulse is retained in the medium within a time interval that is shorter than the irreversible relaxation time of the optically forbidden transition.
Non-classical properties and quantum interference (QI) in two-photon excitation of a three level atom (|1〉), |2〉, |3〉) in a ladder configuration, illuminated by multiple fields in non-classical (squeezed) and/or classical (coherent) states, is studied. Fundamentally new effects associated with quantum correlations in the squeezed fields and QI due to multiple excitation pathways have been observed. Theoretical studies and extrapolations of these findings have revealed possible applications which are far beyond any current capabilities, including ultrafast nonlinear mixing, ultrafast homodyne detection and frequency metrology. The atom used throughout the experiments was Cesium, which was magneto-optically trapped in a vapor cell to produce a Doppler-free sample. For the first part of the work the |1〉 → |2〉 → |3〉 transition (corresponding to the 6S1/2F = 4 → 6P3/2F' = 5 → 6D5/2F = 6 transition) was excited by using the quantum-correlated signal (Ɛs) and idler (Ɛi) output fields of a subthreshold non-degenerate optical parametric oscillator, which was tuned so that the signal and idler fields were resonant with the |1〉 → |2〉 and |2〉 → |3〉 transitions, respectively. In contrast to excitation with classical fields for which the excitation rate as a function of intensity has always an exponent greater than or equal to two, excitation with squeezed-fields has been theoretically predicted to have an exponent that approaches unity for small enough intensities. This was verified experimentally by probing the exponent down to a slope of 1.3, demonstrating for the first time a purely non-classical effect associated with the interaction of squeezed fields and atoms. In the second part excitation of the two-photon transition by three phase coherent fields Ɛ1 , Ɛ2 and Ɛ0, resonant with the dipole |1〉 → |2〉 and |2〉 → |3〉 and quadrupole |1〉 → |3〉 transitions, respectively, is studied. QI in the excited state population is observed due to two alternative excitation pathways. This is equivalent to nonlinear mixing of the three excitation fields by the atom. Realizing that in the experiment the three fields are spaced in frequency over a range of 25 THz, and extending this scheme to other energy triplets and atoms, leads to the discovery that ranges up to 100's of THz can be bridged in a single mixing step. Motivated by these results, a master equation model has been developed for the system and its properties have been extensively studied.
An analytical study of the photon echoes associated with the three-level system interacting resonantly with optical pulses possessing two different frequencies is performed. It is predicted that photon echoes arise at anomalous times corresponding to the correlation between the inhomogeneous broadenings for the different spectral lines as well as at the normal time expected in a simple two-level system. This new effect is caused by the coupling of the two resonant transitions through the common energy level. Furthermore, if the particle does not have inversion symmetry, the echoes with the sum or difference frequency of the exciting optical pulses can be observed in such a system. The quantitative analysis is also given for intensities, direction of propagation and polarizations of the anomalous echoes which depend upon the exciting pulses with different frequency.
The increasing interest in the study of the interaction of several resonant fields with multilevel quantum systems is due to a wide range of possible applications of various effects observed in the multi-frequency excitation of quantum objects. Among them, we can note color echo holography, information compression in three-level environments, copying of quantum information, and multi-level quantum gates that perform logical operations. In addition, the recording and reproduction of echo holograms in multi-level systems leads to the possibility, along with logical operations, to perform a change in the real-time scale and the sequence of events in the echo-hologram response, the data on which were embedded into the temporal structure of the object laser pulse. The formation of optical transient processes in multilevel systems occurs when the short laser pulses separated in time and resonant of different frequency transitions at the substance have an effect on the system, so that their interaction with each other becomes possible only through the medium and only if the medium has a sufficiently long phase memory. In this situation, each laser pulse transmits information about its wave characteristics to the medium, and this information is retained here until the arrival of the next laser pulses. The formation of optical transient processes in a multilevel system in a solid depends essentially on the degree of correlation of the inhomogeneous broadening on different frequency transitions and different time intervals, in connection with the possible destruction of the reversible phase memory of the system due to a partial mutual fixation energies of transitions. The influence of external spatially inhomogeneous electric fields on the resonant medium can lead to an additional artificially created inhomogeneous broadening. In this case, it is possible to control the phase memory of the system by changing the parameters of external spatially inhomogeneous electric fields, and the most pronounced effect on phase memory is the case of laser excitation of narrow frequency regions of inhomogeneously broadened lines of the resonance transitions. Moreover, the artificially created inhomogeneous broadening by external spatially inhomogeneous electric fields due to the Stark effect can be comparable with the spread of frequencies due to a partial mutual fixation of the transition energies, which leads to a partial restoration of the coherence of the multilevel system. This effect can lead to an increase in the intensity of the response of the stimulated photon echo (SPE) in the three-level system, which is the opposite effect of photon echo locking.
The novel variants of the photon echo technique for the storage and complete reconstruction of the quantum states of one and two photon fields are theoretically investigated. Such new possible schemes are proposed for two types of three-level macroscopic coherent media, where the specific spectral and temporal properties of the quantum dynamics are analyzed. Special physical analysis is devoted to the complete reconstruction of the mapped quantum states at the multipulse restoring, its spatial, temporal and spectral properties. The specific possibilities of the proposed schemes for the quantum computations are also discussed. (Summary only available)