Lehmann-Symanzik-Zimmermann reduction approach to multiphoton scattering in coupled-resonator arrays

Shi, Ting-Yun; Sun, C. P.

doi:10.1103/physrevb.79.205111

Cited by 170 publications

(129 citation statements)

References 38 publications

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“…Here, the site x 0 to which the scatterer is coupled is explicitly excluded from the summation since any excitation which might be trapped [14] either does not contribute to propagating modes or, for realistic systems, eventually decays into a loss channel in the long-time limit. Expression (20) has to be evaluated for times after the wave packets have scattered at the impurity but before the reflected and transmitted pulses are influenced by the system's hard-wall boundaries (for details we refer to Ref. [8]).…”

Section: Time Evolution Initial States and Physical Quantitiesmentioning

confidence: 99%

“…Even though losses of T 1 -type lead to irreversible photon loss, the single-photon limit is independent of the value of T 1 because of the normalization of Eq. (20). The black dashed curve represents the lossless case in which T 1 = ∞.…”

Section: From the Harmonic Oscillator To The Two-level Systemmentioning

confidence: 99%

“…[22,23], all wave function trajectories enter the expectation values in Eq. (20), including those that represent zero coincidences.…”

Section: Influence Of Dissipation and Dephasingmentioning

confidence: 99%

See 2 more Smart Citations

The Hong-Ou-Mandel effect in the context of few-photon scattering

Longo¹,

Cole²,

Busch³

2012

Opt. Express

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Abstract:The Hong-Ou-Mandel effect is studied in the context of twophoton transport in a one-dimensional waveguide with a single scatterer. We numerically investigate the scattering problem within a time-dependent, wave-function-based framework. Depending on the realization of the scatterer and its properties, we calculate the joint probability of finding both photons on either side of the waveguide after scattering. We specifically point out how Hong-Ou-Mandel interferometry techniques could be exploited to identify effective photon-photon interactions which are mediated by the scatterer. The Hong-Ou-Mandel dip is discussed in detail for the case of a single two-level atom embedded in the waveguide, and dissipation and dephasing are taken into account by means of a quantum jump approach.

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Section: Time Evolution Initial States and Physical Quantitiesmentioning

confidence: 99%

Section: From the Harmonic Oscillator To The Two-level Systemmentioning

confidence: 99%

See 1 more Smart Citation

The Hong-Ou-Mandel effect in the context of few-photon scattering

Longo¹,

Cole²,

Busch³

2012

Opt. Express

View full text Add to dashboard Cite

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“…An important task is to develop efficient analytical or numerical techniques for modelling the nonequilibrium quantum dynamics of strongly interacting photons. Recent work in this area focused on applying field-theoretical or condensed-matter techniques, such as S-matrix scattering [93][94][95] or density matrix renormalization group 92 .…”

Section: Many-body Physics With Strongly Interacting Photonsmentioning

confidence: 99%

Quantum nonlinear optics — photon by photon

2014

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other. This linearity in light propagation, in combination with the high frequency and hence large bandwidth provided by waves at optical frequencies, has made optical signals the preferred method for communicating information over long distances. In contrast, the processing of information requires some form of interaction between signals. In the case of light, such interactions can be enabled by nonlinear optical processes. These processes, which are now found ubiquitously throughout science and technology, include optical modulation and switching, nonlinear spectroscopy and frequency conversion 1 , and have applications across both the physical 2 and biological 3,4 sciences.A long-standing goal in optical science has been the implementation of nonlinear effects at progressively lower light powers or pulse energies. The ultimate limit may be termed 'quantum nonlinear optics' (Box 1) -the regime where individual photons interact so strongly with one another that the propagation of light pulses containing one, two or more photons varies substantially with photon number. Although this domain is difficult to reach owing to the small nonlinear coefficients of bulk optical materials, the potential payoff is significant. The realization of quantum nonlinear optics could improve the performance of classical nonlinear devices, enabling, for example, fast energy-efficient optical transistors that avoid Ohmic heating 5 . Furthermore, nonlinear switches activated by single photons could enable optical quantum information processing and communication 6 , as well as other applications that rely on the generation and manipulation of non-classical light fields 7,8 . The challenge of making photons interactAt low optical powers, most optical materials exhibit only linear optical phenomena, such as refraction and absorption, which can be described by a complex index of refraction. However, a sufficiently intense light beam can modify a material's index of refraction, such that the light propagation becomes power-dependent. This is the essence of classical nonlinear optics (Box 1). Large optical fields are required to alter the index of refraction of conventional bulk materials because a strong nonlinear response can only be induced if the electric field of the light beam acting on the electrons is comparable to the field of the nucleus. As a result, early experimental observations of nonlinear optical phenomena, such as frequencydoubling or sum-frequency generation 9 , were achievable only after the development of powerful lasers. Advances in nonlinear optics over the past four decades have resulted in progressively more efficient nonlinear processes 10 , thus enabling the observation of nonlinear processes at lower and lower light levels. It is natural to inquire if and how these nonlinear interactions can be made so strong that they become important even at the level of individual quanta of radiation. Although this question was addressed in early theoretical studies [11][12][13] , it has become more pressing with the advent of...

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“…For this reason, people have done many works to generate strongly interacted photons [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Recently, the scheme that a two level system (TLS) coupled to a one-dimensional (1D) continuum has attracted people's attention [7][8][9][10][11][12]. The photons scattering from the localized TLS can be correlated strongly due to the local interaction at TSL (corresponds to the bound state).…”

Section: Introductionmentioning

confidence: 99%

Control of Two-Photon Transport in a One-Dimensional Waveguide

2012

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We study the system consisting of a one-dimension waveguide side-coupled to a nonlinear cavity which was doped with a lambda-type atom and investigate the control of photons transport in one-dimension waveguide through manipulating the atom contained in the cavity. Employing the polariton technique, we show that in the single-photon case, the system behaves as a waveguide coupled to a two-level system. By solving the Schrödinger equation, we show that single photon switch can be achieved by tuning the Rabi frequency of the classical field. In the two-photon case, the system behaves like a waveguide coupled to a cascade three-level system. Two-photon quantum correlation in the position variation can be controlled by adjusting the Rabi frequency.

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Lehmann-Symanzik-Zimmermann reduction approach to multiphoton scattering in coupled-resonator arrays

Cited by 170 publications

References 38 publications

The Hong-Ou-Mandel effect in the context of few-photon scattering

The Hong-Ou-Mandel effect in the context of few-photon scattering

Quantum nonlinear optics — photon by photon

Control of Two-Photon Transport in a One-Dimensional Waveguide

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