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Physical Review A

Propagation of squeezed-light pulses in dispersive and absorbing linear dielectrics

Eduard Schmidt, L. Knöll, Dirk‐Gunnar Welsch

Published Jul 1, 1996• 17 citations

Abstract

The behavior of short quantum light pulses propagating in dispersive and absorbing linear ground-state dielectrics is studied, with special emphasis on squeezed pulses. The analysis is based on normally ordered correlation functions of the electric-field strength, which are related to quantities at the entrance plane, on using quantum Langevin equations. Using nonmonochromatic-mode expansion and restricting attention to a single-mode pulse in a squeezed state, the influence on squeezing of the pulse propagation in the medium is discussed in both the time and frequency domains, and it is shown that the noise reduction observable in homodyne detection sensitively depends on the phase control used. Effects, such as squeezing enhancement associated with pulse compression and the destructive influence of the spectral shift caused by absorption, are demonstrated. The numerical results are supplemented by analytical estimations derived for narrow-bandwidth Gaussian pulses. \textcopyright{} 1996 The American Physical Society.

DOI: 10.1103/physreva.54.843

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The behavior of short quantum light pulses propagating in dispersive and absorbing linear ground-state dielectrics is studied, with special emphasis on squeezed pulses. The analysis is based on normally ordered correlation functions of the electric-field strength, which are related to quantities at the entrance plane, on using quantum Langevin equations. Using nonmonochromatic-mode expansion and restricting attention to a single-mode pulse in a squeezed state, the influence on squeezing of the pulse propagation in the medium is discussed in both the time and frequency domains, and it is shown that the noise reduction observable in homodyne detection sensitively depends on the phase control used. Effects, such as squeezing enhancement associated with pulse compression and the destructive influence of the spectral shift caused by absorption, are demonstrated. The numerical results are supplemented by analytical estimations derived for narrow-bandwidth Gaussian pulses. \textcopyright{} 1996 The American Physical Society.

The systematic theory of the formation of the short light pulses in the squeezed state during the propagation in a medium with inertial Kerr nonlinearity is developed. The algebra of time-dependent Bose-operators is elaborated and the normal-ordering theorem for them is formulated. It is established that the spectral region where the quadrature fluctuations are weaker than the shot-noise, depends on both the relaxation time of the nonlinearity and the magnitude of the nonlinear phase shift. It is also shown that the frequency at which suppression of the fluctuation is greatest can be controlled by adjusting the phase of the initial coherent light pulse. The spectral correlation function of photons is introduced and photon antibunching is found.

Squeezed light is a key resource in quantum metrology and quantum information science. It is primarily generated through nonlinear optical interactions, where the degree of squeezing is set by the nonlinearity of the medium. Here, we modulate the third-order nonlinear response of a dielectric with strong ultrafast laser fields to control squeezed light generation on attosecond time scales. By tuning a sub-cycle phase delay between the input femtosecond pulses, we switch the generated light between amplitude-squeezed and phase-squeezed states. We measure the quantum noise using a frequency-resolved balanced homodyne detection scheme that extracts field quadratures in many frequency modes simultaneously. From these measurements we obtain the complete coherency matrix containing quadrature correlations across the frequency modes of the pulse. These results enable quantum light sources with sub-cycle control of squeezing and open a route to transduction of dynamical quantum correlations in matter to quantum correlations in electric fields.

Squeezing in both intracavity and travelling-wave multiphoton absorption is investigated theoretically for incident intense nearly coherent light. It is shown that after sufficiently strong travelling-wave k-photon absorption (k=2,3...) a squeezed state of the radiation field is reached that is not a minimum uncertainty state. In this state the inphase and quadrature variances of the normalized electric field strength approach the asymptotic values k/(4(2k-1)) and k/4, respectively. With the help of an approximate Heisenberg picture treatment of a continuous mode field travelling through a broad-band k-photon absorber an analytical expression is obtained for the evolution of the squeezing spectrum in dependence on the degree of absorption. For intracavity multiphoton absorption the spectrum of output squeezing is investigated with the help of the usual Langevin equation approach. It turns out that the squeezing bandwidth in intracavity and travelling-wave multiphoton absorption is determined by the cavity bandwidth and the absorber linewidth, respectively.

The problem of decorrelation of entangled (squeezed-vacuum-type) light pulses of arbitrary shape passing through dispersive and absorbing four-port devices of arbitrary frequency response is studied, applying recently obtained results on quantum-state transformation (L Knöll et al 1999 Phys. Rev. A 59 4716). The fidelity and indices of (quantum) correlation based on the von Neumann entropy are calculated, with special emphasis on the dependence on the mean photon number, the pulse shape and the frequency response of the devices. In particular, it is shown that the quantum correlations can decay very rapidly due to dispersion and absorption, and the degree of degradation intensifies with increasing mean photon number.

We present a canonical quantum theory of radiation in nonlinear media taking into account the effects of linear dispersion and absorption in a consistent way. We start from a microscopic model and apply recently developed concepts of the quantization of radiation in dispersive and absorbing linear media and extend the theory in order to include nonlinear optical processes. We derive propagation equations in space and time for the quantized radiation field, with special emphasis on the propagation of quantum-light pulses in Kerr media. In particular, the method enables us to derive systematically the noise sources that arise naturally in the nonlinear terms.