Coherent excitation of a two-level atom driven by a far-off-resonant classical field: Analytical solutions

Jha, Panka J. K.; Rostovtsev, Yuri V.

doi:10.1103/physreva.81.033827

Cited by 32 publications

(38 citation statements)

References 45 publications

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“…Started with the famous examples like the Landau-Zener model [9], Rabi problem [4], RoseZener model [5], the problems of finding analytic solutions of driven TLSs have been underway for a long time [10]- [26]. However, most of the known exact solutions of TLSs are expressed in terms of complicated special functions, such as the Gauss hypergeometric function [10][11][12][13][14][15], Weber function [9,16], associated Legendre function [17], Jacobi elliptic function [18], and Heun function [19][20][21][22]. Up to now, only a very few examples of analytically solvable two-level evolutions described only by several of the simplest solutions [4,26], which renders the control strategies more transparent, have been reported.…”

Section: Introductionmentioning

confidence: 99%

Analytical results for a parity-time-symmetric two-level system under synchronous combined modulations

et al. 2017

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We propose a simple method of combined synchronous modulations to generate the analytically exact solutions for a parity-time symmetric two-level system. Such exact solutions are expressible in terms of simple elementary functions and helpful for illuminating some generalizations of appealing concepts originating in the Hermitian system. Some intriguing physical phenomena, such as stabilization of a non-Hermitian system by periodic driving, non-Hermitian analogs of coherent destruction of tunneling (CDT) and complete population inversion (CPI), are demonstrated analytically and confirmed numerically. In addition, by using these exact solutions we derive a pulse area theorem for such non-Hermitian CPI in the parity-time symmetric two-level system. Our results may provide an additional possibility for pulse manipulation and coherent control of the parity-time symmetric two-level system.

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Section: Introductionmentioning

confidence: 99%

Analytical results for a parity-time-symmetric two-level system under synchronous combined modulations

et al. 2017

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“…The Rabi frequency is given by (5) where (1,2) = gµ 0 B (1,2) / √ 2h. The equations of motion for the probability amplitudes C a and C b are given by [22,23] C a = i (t)e iωt C b , (6a)…”

Section: Theorymentioning

confidence: 99%

Experimental observation of carrier-envelope-phase effects by multicycle pulses

Jha

Rostovtsev²,

Li³

et al. 2011

Phys. Rev. A

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We present an experimental and theoretical study of carrier-envelope-phase (CEP) effects on the population transfer between two bound atomic states interacting with pulses consisting of many cycles. Using intense radio-frequency pulse with Rabi frequency of the order of the atomic transition frequency, we investigate the influence of the CEP on the control of phase-dependent multiphoton transitions between the Zeeman sublevels of the ground state of 87 Rb. Our scheme has no limitation on the duration of the pulses. Extending the CEP control to longer pulses creates interesting possibilities to generate pulses with accuracy that is better than the period of optical oscillations.

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“…Of current interest is the interaction between strong broadband electromagnetic fields and atoms, especially laser radiation that is tuned far from resonance. Short pulses can excite coherence on high-frequency transitions that may be used for efficient generation of extreme ultraviolet (XUV) radiation [4][5][6]. Shaped pulses can enhance transient population of excited states [7] or create optimal coherence in two-level systems (TLSs) [8].…”

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confidence: 99%

Coherent control of atomic excitation using off-resonant strong few-cycle pulses

2010

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We study the dynamics of a two-level system driven by an off-resonance few-cycle pulse which has a phase jump φ at t = t 0 , in contrast to many-cycle pulses, under the nonrotating-wave approximation (NRWA). We give a closed form analytical solution for the evolution of the probability amplitude |C a (t)| for the upper level. Using the appropriate pulse parameters like the phase jump φ, jump time t 0 , pulse width τ , frequency ν, and Rabi frequency 0 the population transfer after the pulse is gone can be optimized and, for the pulse considered here, an enhancement factor of 10 6 -10 8 was obtained. Of current interest is the interaction between strong broadband electromagnetic fields and atoms, especially laser radiation that is tuned far from resonance. Short pulses can excite coherence on high-frequency transitions that may be used for efficient generation of extreme ultraviolet (XUV) radiation [4][5][6]. Shaped pulses can enhance transient population of excited states [7] or create optimal coherence in two-level systems (TLSs) [8]. Recently, we have found an analytical solution describing the dynamics of a two-level atom under the action of laser radiation with an arbitrary pulse shape and polarization [9]. Furthermore, we have studied two mechanisms of atomic excitation: multiphoton excitation, and breaking of adiabaticity [4], and we have shown [10] that the latter can be more efficient.The interaction of such ultrashort pulses with a two-level atom under the rotating-wave approximation does not give us the complete picture since the variation of the atomic polarization and population within the optical cycle is not slow. Thus, we should not neglect the contribution of the counter-rotating terms in the Hamiltonian while studying few-cycle-pulse interactions with atomic systems [11][12][13][14][15][16][17][18]. On the other hand, if the fields are not too strong and the variation of the atomic polarization and population within the optical cycle is slow, the rotating-wave approximation (RWA) appears to be a good approximation.In this brief report, we study the interaction of few-cycle pulses (in contrast to many-cycle pulses [19][20][21]) with a TLS. These pulses have a phase jump φ at t = t 0 . Thus, they can be characterized by the parameters peak Rabi frequency 0 , pulse width τ , carrier frequency ν, phase jump φ, and jump moment t 0 along with the pulse envelope (which we have considered Gaussian for the numerical simulation, see Fig. 1). We present an analytical solution for this problem. Using the appropriate characterizing parameters, the population transfer can be optimized and, for the pulse considered here, enhancement by a factor of 10 6 -10 8 was obtained [see Fig. 5(b)]. The equation of motion for the probability amplitudes for the states |a and |b of a two-level atom (TLA) interacting with a classical field is given as [22]wherehω is the energy difference between two levels, ℘ is the atomic dipole moment, E(t) = E(t)cos(νt). In the RWA we let cos(νt)e ±iωt → e ±i t /2, where = ω − ν [23] is t...

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Coherent excitation of a two-level atom driven by a far-off-resonant classical field: Analytical solutions

Cited by 32 publications

References 45 publications

Analytical results for a parity-time-symmetric two-level system under synchronous combined modulations

Analytical results for a parity-time-symmetric two-level system under synchronous combined modulations

Experimental observation of carrier-envelope-phase effects by multicycle pulses

Coherent control of atomic excitation using off-resonant strong few-cycle pulses

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