Quantum filtering for a two-level atom driven by two counter-propagating photons

Dong, Zhiyuan; Amini, Nina H.

doi:10.1007/s11128-019-2258-x

Cited by 19 publications

(15 citation statements)

References 53 publications

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“…The scattering process of N photons on a quantum system was described in the pure-state wavefunction approaches [10,11] and diagrammatic approaches [12][13][14]. Generalized master equations [15][16][17][18][19][20][21] and stochastic master equations [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] were used to study the excitation of the two-level atom interacting with a N photon packets.…”

mentioning

confidence: 99%

From a posteriori to a priori solutions for a two-level system interacting with a single-photon wavepacket

Da̧browska¹

2020

J. Opt. Soc. Am. B

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We present the analytical formulas for the conditional and unconditional states of a two-level atom interacting with a single-photon wavepacket. We express the a priori state of the system by means of the quantum trajectories related to the process of detection of photons in the output field. We give the formulas for the mean number of photons detected up to the given time and we derive the expressions for the mean time of detection of the photons.

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mentioning

confidence: 99%

From a posteriori to a priori solutions for a two-level system interacting with a single-photon wavepacket

Da̧browska¹

2020

J. Opt. Soc. Am. B

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“…On the other hand, if one of them is indeed transmitted, the two output photons are strongly anti-correlated ( Fig. 9(b)), which is similar to the (11,22) case in [29,Fig. 5].…”

Section: Numerical Examplementioning

confidence: 78%

“…Moreover, the relationship between induced photon-photon correlations and the atomic excitation efficiency is analyzed. When a two-level system is driven by two counterpropagating indistinguishable single photons, it is shown in [11] that the maximal excitation probability attains at γ = 5κ for rising exponential pulse shapes, and Ω = 2 * 1.46κ for Gaussian pulse shapes. Recently, the dynamics of two two-level systems (qubits) driven by two counterpropagating input photons is studied in [56].…”

Section: Introductionmentioning

confidence: 99%

On the Response of a Two-Level System to Two-Photon Inputs

Dong¹,

Amini²

2019

SIAM J. Control Optim.

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The purpose of this paper is to study the interaction between a two-level system (qubit) and two continuous-mode photons. Two scenarios are investigated: Case 1, how a two-level system changes the pulse shapes of two input photons propagating in a single input channel; and Case 2, how a two-level system responds to two counter-propagating photons, one in each input channel. By means of a transfer function approach, the steady-state output field states for both cases are derived analytically in both the time and frequency domains. For Case 1, two examples are presented. In Example 1 a two-photon input state of Gaussian pulse shape is used to excite a two-level atom. The joint probability distribution in the time domain and the joint spectra of the output two-photon state are plotted. The simulation demonstrates that in the time domain the atom tends to stretch out the two photons. Moreover, the prominent difference between the joint probability distribution of the output two-photon state and that of the input two-photon state occurs exactly under the setting when the two-level atom is most efficiently excited. In Example 2, a two-photon input state of rising exponential pulse shape is used to excite a two-level atom. Strong anti-correlation of the output two-photon state is observed, which is absent in Example 1 for the Gaussian pulse shape. Such difference indicates that different pulse shapes give rise to drastically different frequency entanglement of the output two-photon state. Example 3 is used to illustrate Case 2, where two counter-propagating single photons of rising exponential pulse shapes are input to a two-level atom. The frequency-dependent Hong-Ou-Mandel (HOM) interference phenomenon is observed. Moreover, when the two output photons are in the same channel, they are anti-correlated. The simulation results base on the analytic forms of output twophoton states are consistent with those based on quantum master or filter equations [43], [11]. Similar physical phenomena have been observed in physical settings such as cavity opto-mechanical systems and Keer nonlinear cavities.

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“…Therefore, it is natural to study the filtering problem of a quantum system driven by a single-photon field state. Single-photon filters were first derived in [24,64], and their multi-photon version was developed in [26,27,65]. In this section, we focus on the single-photon case.…”

Section: Single-photon Filter and Master Equationmentioning

confidence: 99%

“…When a two-level atom is driven by two co-propagating photons of Gaussian pulse shape, numerical simulations in [26] show that the maximum excitation probability is around 0.88 attained at = 2 * 1.46 . Moreover, when a two-level atom is driven by two counter-propagating identical photons, it is shown in [27,28] that the maximum excitation probability is attained at = 5 for rising exponential pulse shapes, and = 2 * 1.46 for the Gaussian pulse shapes. The rest of this article is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Control engineering of continuous-mode single-photon states: a review

Zhang

2021

Control Theory Technol.

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In this survey, we present single-photon states of electromagnetic fields, discuss discrete measurements of a single-photon field, show how a linear quantum system responds to a single-photon input, investigate how a coherent feedback network can be used to manipulate the temporal pulse shape of a single-photon state, present single-photon filter and master equations, and finally discuss the generation of Schrödinger cat states by means of photon addition and subtraction.

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Quantum filtering for a two-level atom driven by two counter-propagating photons

Cited by 19 publications

References 53 publications

From a posteriori to a priori solutions for a two-level system interacting with a single-photon wavepacket

From a posteriori to a priori solutions for a two-level system interacting with a single-photon wavepacket

On the Response of a Two-Level System to Two-Photon Inputs

Control engineering of continuous-mode single-photon states: a review

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