Corrections to the phenomenological relaxation models for open quantum systems

Tokman, M. D.; Erukhimova, Maria

doi:10.1016/j.jlumin.2012.12.035

Cited by 10 publications

(38 citation statements)

References 21 publications

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“…5 To avoid a misunderstanding, it should be emphasized that appearance of the operator ↔ ε here is connected not with the quantum consideration, but with the specific features of formation of the electrodynamic response in a dispersive medium [37][38][39][40]. 6 For possible refinements of this simplest expression, see, e.g., [50].…”

Section: Quantum Description Of the Field In A Transparent Dielectricmentioning

confidence: 99%

“…F is the fluctuation operator (Langevin source), which should be expressed, generally speaking, in terms of the operatorsL mn of Langevin sources for quantum transitions [42,50] from medium dynamics equations (17). The noise properties are specified by the commutation and correlation properties of the operatorsF andF † .…”

Section: Quantum Description Of the Field In A Dissipative Mediummentioning

confidence: 99%

“…Using the Heisenberg equationσ mn = i [Ĥ,σ mn ]/ and allowing for relations (1), (3), (4), and (8), we obtain (see [42,50]…”

Section: Introductionmentioning

confidence: 99%

“…This can be done by supplementing additively the operators of relaxation and Langevin noises (see, e.g., [2,3,42,49,50,[52][53][54][55]) to Eq. (16) of the atomic-system dynamics:…”

Section: Introductionmentioning

confidence: 99%

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Anisotropy-Induced Transparency in Optically Dense Media

Tokman

Erukhimova

2015

Radiophys Quantum El

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The effect of anisotropy-induced transparency, which is analogous to electromagnetically induced transparency in the three-level medium located in a resonance field, is predicted and studied theoretically. This effect is connected with destructive interference between oscillations in different degrees of freedom of an anisotropic medium, which are connected with each other, as radiation propagates at an angle to one of the optical axes in a triaxial or uniaxial crystal. In this case, a hybrid-type polariton is formed in the "transparency window," which combines the quasilongitudinal polarization with the "vacuum" refractive index. Such a wave is excited easily by radiation incident from the vacuum and should have enhanced impedance of coupling with active or nonlinear elements, which can be useful for the creation of small-size optical systems. Due to the interest in quantum-optical effects displayed recently, the regime of anisotropy-induced transparency is considered within the framework of the quantum theory of radiation in an optically dense medium.

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Section: Quantum Description Of the Field In A Transparent Dielectricmentioning

confidence: 99%

Section: Quantum Description Of the Field In A Dissipative Mediummentioning

confidence: 99%

“…Using the Heisenberg equationσ mn = i [Ĥ,σ mn ]/ and allowing for relations (1), (3), (4), and (8), we obtain (see [42,50]…”

Section: Introductionmentioning

confidence: 99%

“…This can be done by supplementing additively the operators of relaxation and Langevin noises (see, e.g., [2,3,42,49,50,[52][53][54][55]) to Eq. (16) of the atomic-system dynamics:…”

Section: Introductionmentioning

confidence: 99%

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Anisotropy-Induced Transparency in Optically Dense Media

Tokman

Erukhimova

2015

Radiophys Quantum El

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“…The problem is that the relaxation model Eq. (7) should be modified if so called secular approximation is violated [28], that will induce modification of the correlation functions for the noise operators. In summary, we have revealed the effect of significant field-induced modification of the quantum radiation noise in a thermal reservoir.…”

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confidence: 99%

Fluctuation-dissipation relation in a resonantly driven quantum medium

Erukhimova

Tokman

2015

Opt. Lett.

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We calculate the radiation noise level associated with the spontaneous emission of a coherently driven medium. The significant field-induced modification of relation between the noise power and damping constant in a thermal reservoir is obtained. The nonlinear noise exchange between different atomic frequencies leads to violation of standard relations dictated by the fluctuation-dissipation theorem.PACS numbers: 42.50. Lc, 42.50.Ct, 42.50.Gy Introduction -Investigation of fluctuations in open systems (both quantum and classical) is important in many different areas of physics being the subject of incessant general physical interest [1][2][3][4][5]. One of the major results in this field is the Fluctuation-Dissipation Theorem (FDT) [6]. The use of the universal relation between relaxation and fluctuation properties of the medium imposed by FDT turned out to be highly fruitful in the theory of radiation-matter interaction [7]. But in its "standard" variant the FDT is not applicable for nonlinear processes that are of great interest. The theory developed in [8] for calculation of polarisation fluctuations in the presence of coherent drive at the combinational frequency seems to be not applicable for the case of resonant interaction with the medium since it is based on the methods of perturbation theory. Meanwhile one of the most interesting applications of the theory of fluctuations is connected specifically with the resonant control of quantum medium. A number of attractive effects of quantum optics, based on preparation and manipulation of nonclassical states of light with the extremely low dispersion of some physical quantities (squeezed, entangled and so on) [9] are related to these processes. The detailed analysis of Langevin sources influence on the preparation of nonclassical states of light in different nonlinear resonance regimes have been carried out in a wide range of papers [10][11][12][13][14][15][16]. But in most of papers the consideration was restricted to the case of zero temperature. So only the principal possibility of suppression of intrinsic quantum fluctuations in dissipative media was investigated. The additional noise having a thermal nature associated with the processes of spontaneous emission in the environment is a major factor that destroys the ideal quantum state of light. The possibility of suppression (squeezing) of "thermal" fluctuations due to the same mechanisms of nonlinear interactions was considered in the paper [17], but the authors used a simplified method estimating the noise source as for non-interacting oscillators.

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The features of a quantum description of radiation in an optically dense medium

2015

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This paper is devoted to the theory of quantum electromagnetic field in an optically dense medium. Self-consistent equations describing interaction between a quantum field and a quantum dielectric medium are obtained from the first principles, i.e., outside a phenomenological description. Using these equations, we found a transformation (of the Bogoliubov transformation type) that converts the operators of the "vacuum" field into operators of collective perturbations of the field and an ensemble of atoms, that is, photons in the medium. Transformation parameter is the refractive index of the wave mode considered. It is shown that besides the energy of the collective electromagnetic field, the energy of photons in the medium includes the energy of the internal degrees of freedom of the substance and the energy of near-field dipole interaction between atoms in the polarized medium. The concept of negative energy photons is introduced on the basis of self-consistent equations.Keywords: Optically dense medium, quantum field, Bogoliubov transformation, photons in the medium 2 cuum). For example, for the medium with polarizability  and refractive index     4 1 2 2    n ck the result obtained within this approach corresponds to the approximation of small optical density, 12 n  . Despite the obvious constraints, this approach can be very effective. The point is that the approximation of small optical depth, i.e., the assumption that 11 n   in a fairly narrow frequency band, does not contradict, in principle, the condition of strong frequency dispersion, 1     n . As an example, we mention the effect of electromagnetically induced transparency (EIT) [24][25][26][27]: which suggests that within the "transparency window" there is a frequency range in which a small group velocity is combined with an almost "vacuum" phase velocity. However, in general (including some of the EIT modes, see [26,27]), the constraint 11 n   is awkward. To our knowledge, the analysis which is free of both the constraints of the phenomenological approach and the small optical density approximation, was carried out only in terms of a two-level model [5,[28][29][30].This paper is devoted to the development of the theory of quantum field in a medium with an arbitrary optical density and an arbitrary energy-level structure. Selecting as the initial model an ensemble of atoms interacting through a collective field, we came to fairly universal operator equations of quantum electrodynamics of a dielectric medium without spatial dispersion. Using these equations, it was found that the exact dispersion relation   k    for photons in the medium corresponds to the quanta of collective excitations of the field and the medium, and the energy   k   of a quantum includes the energy of the macroscopic field, the energy of the internal degrees of freedom, and the energy of the near-field dipole interaction in the polarized medium. It is shown that the operators of creation and annihilation the photon in the medium are related with t...

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Corrections to the phenomenological relaxation models for open quantum systems

Cited by 10 publications

References 21 publications

Anisotropy-Induced Transparency in Optically Dense Media

Anisotropy-Induced Transparency in Optically Dense Media

Fluctuation-dissipation relation in a resonantly driven quantum medium

The features of a quantum description of radiation in an optically dense medium

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