Quantum-state input-output relations for absorbing cavities

cavity is studied, with special emphasis on the absorption losses in the coupling mirror and their influence on the outgoing field. Generalized operator input-output relations are derived, which are used to calculate the Wigner function of the outgoing field. To illustrate the theory, the preparation of the outgoing field in a Schr\"{o}dinger cat-like state is discussed.

Related papers

Quantum-state input–output relations for absorbing cavities

M Khanbekyan, D-G Welsch, A A Semenov +1 more

The quantized electromagnetic field inside and outside an absorbing high- $Q$ cavity is studied, with special emphasis on the absorption losses in the coupling mirror and their influence on the outgoing field. Generalized operator input-output relations are derived, which are used to calculate the Wigner function of the outgoing field. To illustrate the theory, the preparation of the outgoing field in a Schrödinger cat-like state is discussed.The quantized electromagnetic field inside and outside an absorbing high-$Q$ cavity is studied, with special emphasis on the absorption losses in the coupling mirror and their influence on the outgoing field. Generalized operator input-output relations are derived, which are used to calculate the Wigner function of the outgoing field. To illustrate the theory, the preparation of the outgoing field in a Schrödinger cat-like state is discussed.

arXiv:quant-ph/0512184Journal of Optics B Quantum and Semiclassical OpticsNov 22, 20053 citations

QED of lossy cavities: Operator and quantum-state input-output relations

M. Khanbekyan, L. Knöll, D.‐G. Welsch +2 more

Within the framework of exact quantization of the electromagnetic field in dispersing and absorbing media the input-output problem of a high- $Q$ cavity is studied, with special emphasis on the absorption losses in the coupling mirror. As expected, the cavity modes are found to obey quantum Langevin equations, which could be also obtained from quantum noise theories, by appropriately coupling the cavity modes to dissipative systems, including the effect of the mirror-assisted absorption losses. On the contrary, the operator input-output relations obtained in this way would be incomplete in general, as the exact calculation shows. On the basis of the operator input-output relations the problem of extracting the quantum state of an initially excited cavity mode is studied and input-output relations for the $s$ -parametrized phase-space function are derived, with special emphasis on the relation between the Wigner functions of the quantum states of the outgoing field and the cavity field.Within the framework of exact quantization of the electromagnetic field in dispersing and absorbing media the input-output problem of a high-$Q$ cavity is studied, with special emphasis on the absorption losses in the coupling mirror. As expected, the cavity modes are found to obey quantum Langevin equations, which could be also obtained from quantum noise theories, by appropriately coupling the cavity modes to dissipative systems, including the effect of the mirror-assisted absorption losses. On the contrary, the operator input-output relations obtained in this way would be incomplete in general, as the exact calculation shows. On the basis of the operator input-output relations the problem of extracting the quantum state of an initially excited cavity mode is studied and input-output relations for the $s$-parametrized phase-space function are derived, with special emphasis on the relation between the Wigner functions of the quantum states of the outgoing field and the cavity field.

arXiv:quant-ph/0505117Physical Review ANov 18, 200528 citations

Input-output relations in optical cavities: A simple point of view

Andrea Aiello

In this paper, we present a very simple approach to input-output relations in optical cavities, limiting ourselves to one- and two-photon states of the field. After field quantization, we derive the nonunitary transformation between inside and output annihilation and creation operators. Then we express the most general two-photon state generated by inside creation operators, through base states generated by output creation operators. After renormalization of coefficients of the inside two-photon state, we calculate the outside photon-number probability distribution in a general case; then we treat with some detail the single-mode and symmetrical cavity case. We found that the statistics of emitted photons may exhibit either quantum or classical behavior, depending both on source properties and on cavity characteristics.In this paper, we present a very simple approach to input-output relations in optical cavities, limiting ourselves to one- and two-photon states of the field. After field quantization, we derive the nonunitary transformation between inside and output annihilation and creation operators. Then we express the most general two-photon state generated by inside creation operators, through base states generated by output creation operators. After renormalization of coefficients of the inside two-photon state, we calculate the outside photon-number probability distribution in a general case; then we treat with some detail the single-mode and symmetrical cavity case. We found that the statistics of emitted photons may exhibit either quantum or classical behavior, depending both on source properties and on cavity characteristics.

arXiv:quant-ph/9912023Physical Review ANov 15, 200014 citations

Quantum theory of a one-dimensional optical cavity with output coupling. Field quantization

Kikuo Ujihara

The quantum theory of a one-dimensional optical cavity is developed with emphasis on the presence of output coupling. First the resonant mode is defined and calculated classically. Then the field is decomposed into a sequence of modes by introducing an imaginary boundary at a large distance. The mode functions are proved to be orthogonal with respect to an integration with the dielectric constant as a weighting factor. The Hamiltonian of the field is shown to be equivalent to that of a collection of independent harmonic oscillators, the mass of which is a function of the frequency of oscillation. This equivalent of mass appears on normalizing the mode functions and proves to carry information on the structure of the cavity. Quantization of the field is carried out, and the commutation relation for the electric fields inside and outside the cavity is derived. The commutator is composed of an infinite set of derivatives of $\ensuremath{\delta}$ functions, which discloses the effect of the presence of output coupling and that of the small size of the cavity on the radiation field. Also, the commutator is shown to have some properties common with the classical resonant mode, i.e., the property of exponential decay and its rate.The quantum theory of a one-dimensional optical cavity is developed with emphasis on the presence of output coupling. First the resonant mode is defined and calculated classically. Then the field is decomposed into a sequence of modes by introducing an imaginary boundary at a large distance. The mode functions are proved to be orthogonal with respect to an integration with the dielectric constant as a weighting factor. The Hamiltonian of the field is shown to be equivalent to that of a collection of independent harmonic oscillators, the mass of which is a function of the frequency of oscillation. This equivalent of mass appears on normalizing the mode functions and proves to carry information on the structure of the cavity. Quantization of the field is carried out, and the commutation relation for the electric fields inside and outside the cavity is derived. The commutator is composed of an infinite set of derivatives of $\ensuremath{\delta}$ functions, which discloses the effect of the presence of output coupling and that of the small size of the cavity on the radiation field. Also, the commutator is shown to have some properties common with the classical resonant mode, i.e., the property of exponential decay and its rate.

Physical Review AJul 1, 197555 citations

Quantum input-output theory for optical cavities with arbitrary coupling strength: Application to two-photon wave-packet shaping

Michael G. Raymer, Colin J. McKinstrie

We develop quantum-optical input-output theory for resonators with arbitrary coupling strength, and for input fields whose spectrum can be wider than the cavity free-spectral range, while ensuring that the field-operator commutator relations in space-time variables are correct. The cavity-field commutator exhibits a series of space-time ``echoes,'' representing causal connections of certain space-time points by light propagation. We apply the theory to two-photon wave-packet shaping by cavity reflection, which displays a remarkable illustration of dispersion cancellation. We also show that the theory is amenable to inclusion of intracavity absorbing and emitting atoms, allowing, for example, dissipative losses within the cavity to be incorporated in a quantum mechanically correct way.We develop quantum-optical input-output theory for resonators with arbitrary coupling strength, and for input fields whose spectrum can be wider than the cavity free-spectral range, while ensuring that the field-operator commutator relations in space-time variables are correct. The cavity-field commutator exhibits a series of space-time ``echoes,'' representing causal connections of certain space-time points by light propagation. We apply the theory to two-photon wave-packet shaping by cavity reflection, which displays a remarkable illustration of dispersion cancellation. We also show that the theory is amenable to inclusion of intracavity absorbing and emitting atoms, allowing, for example, dissipative losses within the cavity to be incorporated in a quantum mechanically correct way.

arXiv:1309.5915Physical Review AOct 11, 201329 citations

Quantum-optical input-output relations for dispersive and lossy multilayer dielectric plates

Toralf Gruner, D.‐G. Welsch

Using the Green-function approach to the problem of quantization of the phenomenological Maxwell theory, the propagation of quantized radiation through dispersive and absorptive multilayer dielectric plates is studied. Input-output relations are derived, with special emphasis on the determination of the quantum noise generators associated with the absorption of radiation inside the dielectric matter. The input-output relations are used to express arbitrary correlation functions of the outgoing field in terms of correlation functions of the incoming field and those of the noise generators. To illustrate the theory, photons at dielectric tunneling barriers are considered. It is shown that inclusion in the calculations of losses in the photonic band gaps may substantially change the barrier traversal times. \textcopyright{} 1996 The American Physical Society.Using the Green-function approach to the problem of quantization of the phenomenological Maxwell theory, the propagation of quantized radiation through dispersive and absorptive multilayer dielectric plates is studied. Input-output relations are derived, with special emphasis on the determination of the quantum noise generators associated with the absorption of radiation inside the dielectric matter. The input-output relations are used to express arbitrary correlation functions of the outgoing field in terms of correlation functions of the incoming field and those of the noise generators. To illustrate the theory, photons at dielectric tunneling barriers are considered. It is shown that inclusion in the calculations of losses in the photonic band gaps may substantially change the barrier traversal times. \textcopyright{} 1996 The American Physical Society.

Physical Review AAug 1, 1996123 citations

The quantized electromagnetic field inside and outside an absorbing high-

Q

The quantized electromagnetic field inside and outside an absorbing high-

Q

Within the framework of exact quantization of the electromagnetic field in dispersing and absorbing media the input-output problem of a high-

Q

cavity is studied, with special emphasis on the absorption losses in the coupling mirror. As expected, the cavity modes are found to obey quantum Langevin equations, which could be also obtained from quantum noise theories, by appropriately coupling the cavity modes to dissipative systems, including the effect of the mirror-assisted absorption losses. On the contrary, the operator input-output relations obtained in this way would be incomplete in general, as the exact calculation shows. On the basis of the operator input-output relations the problem of extracting the quantum state of an initially excited cavity mode is studied and input-output relations for the

s

-parametrized phase-space function are derived, with special emphasis on the relation between the Wigner functions of the quantum states of the outgoing field and the cavity field.