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Journal of Physics B Atomic Molecular and Optical Physics

Maximum coherent superposition state achievement using a non-resonant pulse train in non-degenerate three-level atoms

Li Deng, Yueping Niu, Luling Jin, Shangqing Gong

Published Oct 4, 2010• 2 citations
Publisher

Abstract

The coherent superposition state of the lower two levels in non-degenerate three-level Λ atoms is investigated using the accumulative effects of non-resonant pulse trains when the repetition period is smaller than the decay time of the upper level. First, using a rectangular pulse train, the accumulative effects are re-examined in the non-resonant two-level atoms and the modified constructive accumulation equation is analytically given. The equation shows that the relative phase and the repetition period are important in the accumulative effect. Next, under the modified equation in the non-degenerate three-level Λ atoms, we show that besides the constructive accumulation effect, the use of the partial constructive accumulation effect can also achieve the steady state of the maximum coherent superposition state of the lower two levels and the latter condition is relatively easier to manipulate. The analysis is verified by numerical calculations. The influence of the external levels in such a case is also considered and we find that it can be avoided effectively. The above analysis is also applicable to pulse trains with arbitrary envelopes.

DOI
10.1088/0953-4075/43/20/205502

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The coherent superposition state of the lower two levels in non-degenerate three-level Λ atoms is investigated using the accumulative effects of non-resonant pulse trains when the repetition period is smaller than the decay time of the upper level. First, using a rectangular pulse train, the accumulative effects are re-examined in the non-resonant two-level atoms and the modified constructive accumulation equation is analytically given. The equation shows that the relative phase and the repetition period are important in the accumulative effect. Next, under the modified equation in the non-degenerate three-level Λ atoms, we show that besides the constructive accumulation effect, the use of the partial constructive accumulation effect can also achieve the steady state of the maximum coherent superposition state of the lower two levels and the latter condition is relatively easier to manipulate. The analysis is verified by numerical calculations. The influence of the external levels in such a case is also considered and we find that it can be avoided effectively. The above analysis is also applicable to pulse trains with arbitrary envelopes.
We investigate coherent accumulation processes in three-level atoms excited by a train of ultrashort pulses in the case where the atomic relaxation times are greater than the laser repetition period. In this situation the resonances of the laser field with the atomic system are determined by the laser frequency comb rather than by the spectrum of a single pulse. Using the density matrix formalism, we develop a perturbative theory that is valid for arbitrary pulse shapes. The excitation of a Doppler-broadened atomic vapor by hyperbolic-secant pulses and $0\ensuremath{\pi}$ pulses is analyzed. It is shown that pulse shape has a great influence on the accumulation process and can change the spectral periodicity of the pattern impressed on the Doppler profile of the medium due to the two-photon absorption process. The effect of interpulse phases is also investigated, and we show that the atomic populations can vary by more than one order of magnitude with small variations of the laser repetition rate, while being insensitive to variations of the laser offset. Finally, the theory is adapted for the temporal-coherent-control technique, and its results are compared with previously reported experimental data.
An assembly of ground-state two-level atoms with a Maxwellian velocity distribution is considered to be illuminated by a near-resonant train of Gaussian pulses whose pulse separation is of the same order of magnitude as the natural decay time of the upper state by spontaneous emission. The equations of motion of the density matrix, including spontaneous decay, are numerically integrated over the duration of one pulse and are analytically integrated between pulses. In this way, the transition matrix is derived. The time evolution of the system is then followed by successive multiplications of the state vector by the transition matrix. Steady state is attained after a few pulses. Because the pulse train has side bands separated by the pulse repetition frequency, corresponding velocity groups are preferentially excited. The response (defined as the time-average spontaneous emission of the assembly) is found to be a quasi-sinusoidal function of the number of Rabi flops per pulse. Frequency modulation of the pulse train leads to smaller variation in the response and, consequently, to considerably higher response.
We study the effects of propagation through an extended sample of two- and three-level atoms on the coherent accumulation of excitation by an ultrashort pulse train. In the two-level case, previous pulses in the train may prepare the medium such that a later pulse may experience amplification and absorption in different positions inside the sample. For a large number of pulses, the atomic medium may be saturated by the train, and some pulses propagate without experiencing either absorption or amplification. In general, absorption of the resonant pulse frequency during propagation compromises the accumulation efficiency. In the three-level case, the coherent accumulation of excitation leads to electromagnetically induced transparency of the pulse train, and the pulses exit the medium without any distortion in their temporal profile.
We investigate the excitation of an atomic degenerate-$\ensuremath{\Lambda}$ system by a train of ultrashort pulses. An iterative analytic solution to the optical Bloch equations is found describing the temporal evolution of the density matrix elements. We show that electromagnetically induced transparency of the excitation pulses develops through the coherent accumulation of excitation (population and coherence) between the degenerate lower states. The influence of the pulse train parameters (area, repetition period, and phase between successive pulses) on establishing the transparency is investigated.
We present a detailed analysis of coherence creation in a four-level double Λ-like atomic system using a train of ultra-short few-cycle Gaussian pulses. The effect of the Doppler broadening has been analyzed. It is possible to create high coherence across all the velocity groups in the atomic ensemble using pulses with low repetition frequency. The accumulation of coherence at different radial locations within the atomic beam cross-section as a function of the number of pulses in the train is also reported. We find that pulse trains with lower repetition frequencies are able to generate high and nearly uniform coherence in a substantial part of the atomic system.
We study the dynamics of three-level $\ensuremath{\Lambda}$-type atoms driven by a coherent train of short, nonoverlapping laser pulses. We derive analytical nonperturbative expressions for the density matrix by approximating the pulses by a $\ensuremath{\delta}$ function. We demonstrate that, depending on the train parameters, several scenarios of system dynamics can be realized. We show the possibility of driving Raman transitions between the two ground states of the $\ensuremath{\Lambda}$ system, avoiding populating excited states by using pulses with effective area equal to $2\ensuremath{\pi}$. The number of $2\ensuremath{\pi}$ pulses needed to transfer the entire population from one ground state to another depends on the ratio between the Rabi frequencies of two allowed transitions. In the case of equal Rabi frequencies, the system can be transferred from one ground state to another with a single $2\ensuremath{\pi}$ pulse. When the total pulse area differs from $2\ensuremath{\pi}$ and the two-photon resonance condition is fulfilled, the system evolves into a ``dark'' state and becomes transparent to subsequent pulses. The third possible scenario is the quasi-steady-state regime when neither the total single-pulse area is equal to $2\ensuremath{\pi}$ nor is the two-photon resonance condition fulfilled. In this regime the radiative-decay-induced drop in the population following a given pulse is fully restored by the subsequent pulse. We derive an analytical expression for the density matrix in the quasi-steady-state regime. We analyze the dependence of the postpulse excited-state population in the quasi-steady-state regime on the train parameters. We find the optimal values for the train parameters corresponding to the maximum of the excited-state population. The maximum of the excited-state population in the steady-state regime is reached at an effective single-pulse area equal to $\ensuremath{\pi}$ and is equal to 2/32/32/3 in the limiting case when its radiative lifetime is much shorter than the pulse repetition period.