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Quantum Coherent Control and Propagation in Lambda System

Pooja Nadkarni Singh

Published May 1, 2016• 0 citations
Publisher

Abstract

Strong coherence in quasi-resonant laser driven system interferes with effective relaxations, resulting in behaviors like, coherent population trapping and Electromagnetically induced transparency. The Raman system can optimize this utilizing excited coherence in the lambda system when exposed to counter- intuitive pump-stokes pulses. The phenomenon can result in complete population transfer between vibrational levels called Stimulated Raman adiabatic passage(STIRAP). STIRAP and CHIRAP have been studied with Gaussian and chirped pulses. The optical propagation effects in dense medium for these phenomenon is studied to calculate the limitations and induced coherences. Further, the effect of rotational levels has been investigated. The molecular vibrational coherence strongly depends on the effect of rotational levels. The change in coherence interaction for ro-vibrational levels are reported and explained. We have considered the effects on the phase of radiation related to rotational mechanical motion of quantum system by taking advantages in ultra strong dispersion medium provided by quantum coherence in lambda system. The enhanced Fizeau effect on a single atom is observed.

DOI
10.12794/metadc849750

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Strong coherence in quasi-resonant laser driven system interferes with effective relaxations, resulting in behaviors like, coherent population trapping and Electromagnetically induced transparency. The Raman system can optimize this utilizing excited coherence in the lambda system when exposed to counter- intuitive pump-stokes pulses. The phenomenon can result in complete population transfer between vibrational levels called Stimulated Raman adiabatic passage(STIRAP). STIRAP and CHIRAP have been studied with Gaussian and chirped pulses. The optical propagation effects in dense medium for these phenomenon is studied to calculate the limitations and induced coherences. Further, the effect of rotational levels has been investigated. The molecular vibrational coherence strongly depends on the effect of rotational levels. The change in coherence interaction for ro-vibrational levels are reported and explained. We have considered the effects on the phase of radiation related to rotational mechanical motion of quantum system by taking advantages in ultra strong dispersion medium provided by quantum coherence in lambda system. The enhanced Fizeau effect on a single atom is observed.
Quantum coherence and interference in atomic systems can lead to interesting optical phenomena such as nonabsorbing resonances, lasing without inversion, generating an ultrahigh index of refraction without absorption, propagation of light pulses without losses. In the last-named is given the title transparency. Up to now it is known some types of transparency in multi-level resonant media. One of them is electromagnetically induced transparency (EIT). The phenomenon of EIT in the propagation of laser radiation through an absorbing medium has been recently investigated and explained in terms of quantum coherence and interference for multi-level atomic system. For instance in the (Lambda) -system, if the atomic medium is prepared in a quantum superposition of states, matched pulses, i.e., a pair of optical pulses whose amplitude and phase have a well defined relation, propagate without absorption. The mechanism of coherent population trapping is responsible for EIT in a (Lambda) -system. There is another, well known mechanism for creating transparency in a two-state atom: self-induced transparency, or SIT. Here, a single pulse whose area (the integral of its Rabi frequency over time) is 2(pi) is applied to the medium. Such a pulse causes the atoms to cycle smoothly from the ground to the excited state and then back again. In principle, such a pulse can propagate over long distances. SIT can be generalized to multi-level systems and multiple quasi-monochromatic fields. Generalization of SIT in a (Lambda) -system was obtained in reference 2. In this report we present a new type of transparency (combined transparency). This type describes propagation of laser pulse through a (Lambda) -type medium where the initial atomic state is prepared in the form of spatially varying coherent superposition of low-energetic states (initial coherency gradient). The common envelope behaves as usual 2(pi) hyperbolic secant pulse, but the ratio between the components of frequencies transitions 1> yields 3> and 2> yields 3> changes due to coherent Raman scattering so (phi) equals atan(E1/E2) equals (pi) /2-Gz, where z is the coordinate, G is the constant determined by both the incident pulse parameters and the initial coherence between the atomic states. Our solution demonstrates a direct connection of EIT in adiabatic regime to the SIT effects. This type of a transparency is given the title screw-type transparency, because for the given form of incident pulse (pitch of screw) medium is transparent, if medium's the initial coherence gradient is correspondingly prepared (thread on a engine nut). Besides a transparency, this phenomenon contains a transformation of the incident pulse frequency during the process of the propagation. This property of the phenomena can be result in a complete conversion of the frequency.
A novel chirped pulse control scheme is presented based on Coherent Anti-Stokes Raman Spectroscopy (C-CARS) aiming at maximizing the vibrational coherence in atoms and molecules. The scheme utilizes chirping of the three incoming pulses, the pump, the Stokes and the probe, in the four-wave mixing process of C-CARS to fulfill the adiabatic passage conditions. The derivation of the scheme is based on simplifying the four-level system into a 'super-effective' two level system via rotating wave approximation and adiabatic elimination of the excited state manifold. The robustness, spectral selectivity and adiabatic nature of C-CARS method may prove useful for sensing, imaging, and detection. It is demonstrated that the selectivity in excitation of vibrational degrees of freedom can be controlled by carefully choosing the spectral chirp rate of the pulses. The C-CARS control scheme is applied to a surrogate methanol molecule to generate an optimal anti-Stokes signal backscattered from a cloud of molecules a kilometer away. The theory is based on the solution of the coupled Maxwell-Liouville von Neumann equations and focuses on the quantum effects induced in the target molecules by the control pulse trains. The propagation effects of pulses through the medium are evaluated and the buildup of the molecular-specific anti-Stokes signal is demonstrated numerically. A deep learning technique, using Convolutional Neural Networks (CNN), is implemented to characterize the control pulses and evaluate time-dependent phase characteristics from them. The effects of decoherence induced by spontaneous decay and collisional dephasing are also examined. Additionally, we present the technique of Fractional Stimulated Raman Adiabatic Passage (F-STIRAP) and demonstrate that it can be utilized for remote detection in a multi-level system by creation of a maximally coherent superposition state.
We have theoretically investigated the vibrational population transfer in the presence of manifolds of rotational levels in a model 15-level Li2{\text{Li}}_{2}Li2​ molecular system by stimulated Raman adiabatic passage with intense unchirped femtosecond laser pulses. We have considered five rotational levels Jg=0,2,…,8{J}_{g}=0,2,\dots{},8Jg​=0,2,…,8 associated with the initial vibrational level vg=0{v}_{g}=0vg​=0 of the ground electronic state $X\text{ }{^{1}\ensuremath{\Sigma}}_{g}^{+}$, five rotational levels Ji=1,3,…,9{J}_{i}=1,3,\dots{},9Ji​=1,3,…,9 associated with the vibrational level vi=1{v}_{i}=1vi​=1 of the intermediate excited electronic state $A\text{ }{^{1}\ensuremath{\Sigma}}_{u}^{+}$, and five rotational levels Jf=0,2,…,8{J}_{f}=0,2,\dots{},8Jf​=0,2,…,8 associated with the final target vibrational levels vf=1,2{v}_{f}=1,2vf​=1,2 of the $X\text{ }{^{1}\ensuremath{\Sigma}}_{g}^{+}$ state of the Li2{\text{Li}}_{2}Li2​ alkali dimer. The pump and Stokes laser pulses are taken to have the same temporal (Gaussian) shapes, pulse widths, and linear parallel polarizations. The laser wavelengths are in the (visible) range of 700--740 nm. The (peak) intensities of the pulses are of the order of $1\ifmmode\times\else\texttimes\fi{}{10}^{12}--2.5\ifmmode\times\else\texttimes\fi{}{10}^{13}\text{ }\text{W}/{\text{cm}}^{2}$ and the pulse widths are of the order of 20--50 fs. We have solved the 15 coupled time-dependent Schr\"odinger equations to study the population transfer to the target-excited vibrational levels. We have observed that, even with ``mushrooming'' of closely spaced rotational levels, efficient and selective population transfer to excited vibrational levels in Li2{\text{Li}}_{2}Li2​ alkali dimer can be achieved for counterintuitive pulse sequence by controlling the pump and Stokes laser parameters. We have endeavored to explain the results within the framework of adiabatic picture.
The spatial and temporal dynamics of two short pulses propagating in an optically dense medium of resonant three-level Λ-atoms is investigated numerically and analytically. The maximum coherence for the Raman transition due to coherent population trapping. It is shown that, at the initial stage of propagation, the waveforms of such pulses only slightly change along the length of the medium, which may considerably exceed the length of linear absorption for a single weak pulse. As the length of the absorbing medium increases, the energy of the probe (first) pulse is completely transferred into the second (control) pulse.
We have considered a coherent population transfer to a higher excited singlet state ( S2 ) of molecules with anomalous fluorescence in molecular assemblies (e.g., a dense medium). A direct excitation to S2 requires light in the UV region. Because of this, the transition is conveniently realized by a two-step (two-photon) process: S0→S1→S2 , where transitions S0→S1 and S1→S2 correspond to the optical region. We have shown that efficient stimulated Raman adiabatic passage (STIRAP) in the ladder configuration can be realized in this case, using suitably chirped pulses, to compensate a change of the two-photon transition frequency in time, induced by the pulses themselves, due to near dipole-dipole interactions. We have provided a reduced state formulation of the optical control process. Chirping the “pump” pulse that excites transition S0→S1 is nonequivalent to chirping the “Stokes” pulse that excites transition S1→S2 , with respect to the population of the intermediate state ( S1 ) in the pulse nonadiabatic regime. We have also shown that with suitably chirped pulses, efficient STIRAP still persists even for a rather large decay of the intermediate state.
The effect of the collisions on the control of coherent population transfer in a closed inverse YYY-type four-level system driven by three laser fields is investigated with the stimulated Raman adiabatic passage technique. An arbitrary coherent superposition between the initial state and target state can be created either by varying the Rabi frequency of the control laser field or by tuning the one-photon detunings of the pump and Stokes laser fields. When the three laser fields with nearly equal peak Rabi frequencies are each tuned to resonance with the respective transitions, the low transfer efficiency due to the nonadiabatic coupling between two degenerate adiabatic states could be enhanced dramatically with the increase of the collision-induced coherence decay rates to the value nearly comparable to the Rabi frequency of the control field. The enhanced transfer efficiency results from the collision-controlled electromagnetically induced transparency in the $\ensuremath{\Lambda}$-type three-level subsystem and electromagnetically induced absorption in the ladder-type three-level subsystem of the four-level system.