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Chinese Physics Letters

Optical Nutation Effect in the Three-Level System Driven by a Coherent Microwave Field

Zhuo‐Liang Cao, Guo Guang-Can

Published Aug 1, 1997• 1 citation
Publisher

Abstract

In this paper, a coherent transient effect–optical nutation in Bloch form is studied semiclassically in the three-level atomic system driven by a coherent microwave field. The amplitude of the optical nutation signal field is obtained. It is found that the signal field, related to the microwave, is the overlap of two slow oscillations instead of one.

DOI
10.1088/0256-307x/14/8/008

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In this paper, a coherent transient effect–optical nutation in Bloch form is studied semiclassically in the three-level atomic system driven by a coherent microwave field. The amplitude of the optical nutation signal field is obtained. It is found that the signal field, related to the microwave, is the overlap of two slow oscillations instead of one.
We analyze the transient response induced by a resonant, weak probe laser in a three-level V-type system driven by a strong, resonant coupling laser. The Rabi oscillation of the probe transition contains two frequencies determined by the coupling laser, and the ratio of the two-frequency components can be controlled by a time delay between the probe and the coupling laser. In particular, when both lasers are turned on simultaneously, the optical nutation with the frequency approximately equal to the Rabi frequency of the coupling laser is dominant; when the probe laser is turned on well after the steady state is reached for the coupling transition, the Rabi oscillation of the probe transition still occurs, and the oscillatory frequency is approximately equal to half of the Rabi frequency of the coupling laser. When both the probe and the coupling lasers are strong, the mutual interaction of the two fields and the atomic system may revive the optical nutation with each other.
A theoretical analysis of the optical coherent transients that arise when a sample of two-level atoms is irradiated by a sequence of three broad-bandwidth pulses is presented. The first two pulses have a relative delay time of order of the correlation time of the pulse fluctuations and are sent into an atomic vapor from different directions. These pulses, whose temporal width is much greater than the delay time, can be correlated with one another and can be strong enough to saturate the two-level atomic transition. The third pulse is weak, noncorrelated with the first two, and is delayed in time so that it does not overlap them. We present a detailed examination of the transient signal that is produced when the third pulse is scattered by the spatial gratings in the population difference of atoms created by the first two pulses. Taking into account the effects of inhomogeneous and homogeneous broadening, we calculate the intensity of the transient signal, emitted in different directions, as a function of delay time. The signal is found to depend dramatically on the intensities of the excitation pulses. It is shown that, for strong excitation pulses, there is a direct dependence of the signal on the cross-correlation time of pulses ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}$ that does not exist when the pulses are weak. In particular, the strongest signals exhibit a peak of width of order ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}$. This peak can have a very narrow dip near its maximum whose width is much smaller than ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}$, if the pulses are fully correlated. We develop a representation of the time evolution of the Bloch vector of a two-level atom, driven by time-delayed pulses, that enables us to explain our results. In this representation, the two time-delayed pulses are replaced by two fully overlapping pulses having some effective amplitudes and atomic field detunings.
The dynamics of a two-level spin system dressed by bichromatic radiation is studied under the conditions of double resonance when the frequency of one (microwave) field is equal to the Larmor frequency of the spin system and the frequency of the other (radio-frequency) field ω rf is close to the Rabi frequency ω 1 in a microwave field. It is shown theoretically that Rabi oscillations between dressed-spin states with the frequency ɛ are accompanied by higher-frequency oscillations at frequencies n ω rf and n ω rf ± ɛ, where n = 1, 2,.... The most intense among these are the signals corresponding to n = 1. The counter-rotating (antiresonance) components of the RF field give rise to a shift of the dressed-state energy, i.e., to a frequency shift similar to the Bloch-Siegert shift. In particular, this shift is manifested as the dependence of the Rabi-oscillation frequency ɛ on the sign of the detuning ω 1 − ω rf from resonance. In the case of double resonance, the oscillation amplitude is asymmetric; i.e., the amplitude at the sum frequency ω rf + ɛ increases, while the amplitude at the difference frequency ω rf − ɛ decreases. The predicted effects are confirmed by observations of the nutation signals of the electron paramagnetic resonance (EPR) of E ′ 1 centers in quartz and should be taken into account to realize qubits with a low Rabi frequency in solids.
We discuss the dynamics of a three-level V-type atom driven simultaneously by a cavity photon and microwave field by examining the atomic population evolution. Owing to the coupling effect of the cavity photon, periodical oscillation of the population between the two upper states and the ground state takes place, which is the well-known vacuum Rabi oscillation. Meanwhile, the population exchange between the upmost level and the middle level can occur due to the driving action of the external microwave field. The general dynamic behavior is the superposition of a fast and a slow periodical oscillation under the cooperative and competitive effect of the cavity photon and the microwave field. Numerical results demonstrate that the time evolution of the population is strongly dependent on the atom–cavity coupling coefficient g and Rabi frequency ?_e that reflects the intensity of the external microwave field. By modulating the two parameters g and ?_e, a large number of population transfer behaviors can be achieved.
We discuss the dynamics of a three-level V-type atom driven simultaneously by a cavity photon and microwave field by examining the atomic population evolution. Owing to the coupling effect of the cavity photon, periodical oscillation of the population between the two upper states and the ground state takes place, which is the well-known vacuum Rabi oscillation. Meanwhile, the population exchange between the upmost level and the middle level can occur due to the driving action of the external microwave field. The general dynamic behavior is the superposition of a fast and a slow periodical oscillation under the cooperative and competitive effect of the cavity photon and the microwave field. Numerical results demonstrate that the time evolution of the population is strongly dependent on the atom–cavity coupling coefficient g and Rabi frequency Ω e that reflects the intensity of the external microwave field. By modulating the two parameters g and Ω e , a large number of population transfer behaviors can be achieved.