Atomic systems optical coherence

Abstract. A suitable femtosecond (fs) laser system can provide a broad band comb of stable optical frequencies and thus can serve as an rf/optical coherent link. In this way we have performed a direct comparison of the IS — 2S transition in atomic hydrogen at 121 nm with a cesium fountain clock, built at the LPTF/Paris, to reach an accuracy of 1.9 x 10-14. The same comb-line counting technique was exploited to determine and recalibrate several important optical frequency standards. In particular, the improved measurement of the Cesium Di line is necessary for a more precise determination of the fine structure constant. In addition, several of the best-known optical frequency standards have been recalibrated via the fs method. By creating an octave-spanning frequency comb a single-laser frequency chain has been realized and tested. 

Quantum optical experiments, by which we mean the investigation of the interaction between simple quantum systems and coherent light, have proven to be a successful tool to test basic concepts in quantum mechanics. Most of the experiments to date were performed with atoms or ions in vapors, beams or traps. An attractive feature of atoms relates to their relatively simple structure which is theoretically fairly well understood. 

The atomic coherence and interference phenomenon in the simple three-level system sueh as EIT can be extended to more eomplicated multi-level atomic systems. A variety of other phenomena and applications involving three or four-level EIT systems have been studied in reeent years. In particular, phase-dependent atomic coherence and interference has been explored [52-66]. These studies show that in multi-level atomic systems coupled by multiple laser fields, there are often various types of nonlinear optical transitions involving multiple laser fields and the quantum interference among these transition paths may exhibit complicated spectral and dynamic features that can be manipulated with the system parameters such as the laser field amplitudes and phases. Here we present two examples of such coherently coupled multi-level atomic systems in which the quantum interference is induced between two nonlinear transition paths and can be eontrolled by the relative phase of the laser fields. 

Phase-dependent coherence and interference can be induced in a multi-level atomic system coupled by multiple laser fields. Two simple examples are presented here, a three-level A-type system coupled by four laser fields and a four-level double A-type system coupled also by four laser fields. The four laser fields induce the coherent nonlinear optical processes and open multiple transitions channels. The quantum interference among the multiple channels depends on the relative phase difference of the laser fields. Simple experiments show that constructive or destructive interference associated with multiple two-photon Raman channels in the two coherently coupled systems can be controlled by the relative phase of the laser fields. Rich spectral features exhibiting multiple transparency windows and absorption peaks are observed. The multicolor EIT-type system may be useful for a variety of application in coherent nonlinear optics and quantum optics such as manipulation of group velocities of multicolor, multiple light pulses, for optical switching at ultra-low light intensities, for precision spectroscopic measurements, and for phase control of the quantum state manipulation and quantum memory. 

To summarize, we have studied the interaction of two weak quantum fields with an optically dense medium of coherently driven four-level atoms in tripod configuration. We have presented a detailed semiclassical as well as quantum analysis of the system. The main conclusion that has emerged from this study is that optically dense vapors of tripod atoms are capable of realizing a novel regime of symmetric, extremely efficient nonlinear interaction of two multimode single-photon pulses, whereby the combined state of the system acquires a large conditional phase shift that can easily exceed 1r. Thus our scheme may pave the way to photon-based quantum information applications, such as deterministic all-optical quantum computation, dense coding and teleportation [Nielsen 2000]. We have also analyzed the behavior of the multimode coherent state and shown that the restriction on the classical correspondence of the coherent states severely limits their usefulness for QI applications. 

It is worth noting that the four-fold symmetry of hexadecapole moment is revealed only at the synchronous pumping and, what is important, at time moments when the hexadecapole moment is precisely aligned with one of its symmetry axis along the linear polarization of the field and the atomic coherence p 2, 2 in the M-system has its maximal value. The periodic change of the optical properties of atomic medium modulates the angle of tight polarization that leads to the FM NMOR resonances. If the time-dependent optical rotation is measured at the first harmonic of (.lm, a resonance is seen when Qm = k Ql which allows one to separate the NFS produced by different atomic PM. Indeed, in the experiment the in-phase and quadrature amplitudes of optical rotation,... 

In conclusion, we have presented a reliable method for selective production and detection of high-order atomic polarization moments based on the nonlinear magneto-optical effects with frequency modulated light. This method can be used for the selective control of higher order atomic coherences in multilevel systems exploiting large Kerr nonlinearities for the construction of all-optical quantum phase gates. 

Schemes of coherent control [Shapiro 2003] and quantum information processing [Cirac 1995 Mplmer 1999 Sackett 2000] that are based on optically-manipulated atoms face the challenge of protecting the quantum states of the system from decoherence, or fidelity loss, due to atomic spontaneous emis-...

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