Spectra of Ultrabroadband Squeezed Pulses and the Finite-Time Unruh-Davies Effect

Abstract

We study spectral properties of quantum radiation of ultimately short duration. In particular, we introduce a continuous multimode squeezing operator for the description of subcycle pulses of entangled photons generated by a coherent-field driving in a thin nonlinear crystal with second order susceptibility. We find the ultrabroadband spectra of the emitted quantum radiation perturbatively in the strength of the driving field. These spectra can be related to the spectra expected in an Unruh-Davies experiment with a finite time of acceleration. In the time domain, we describe the corresponding behavior of the normally ordered electric field variance. PACS numbers: 42.50.Dv, 42.50.Lc, 42.65.Re, 04.62.+v Introduction.-In quantum optics, parametric downconversion (PDC) in nonlinear crystals (NXs) has been routinely used to generate pairs of monochromatic entangled photons [1,2]. The so obtained squeezed states of light have found applications in a broad range of areas like gravitational wave detection [3,4], quantum communication systems [5][6][7] and precision measurements [8,9]. The active interest in squeezed states can be mainly related to the fact that the variance of a given phase space quadrature (a quantum-optical analogue of a canonical variable) is lower for a squeezed state than for a coherent state, including the vacuum state itself. In order to fulfill Heisenberg's uncertainty principle the variance of the conjugate quadrature exhibits the opposite behavior.In recent years, theoretical and experimental efforts have been made to describe and generate multimode squeezed states [10][11][12][13][14][15]. Although they have already been experimentally realized by a number of groups [12,15], most of the achievements so far are limited to squeezed states with relatively narrow spectra, where the central frequency approximation is still valid. New developments in ultra-stable few-cycle laser sources and advanced detection techniques have paved the way for the generation of few-cycle pulses of mid-infrared (MIR) squeezed light and the electro-optic detection of their electric field statistics with subcycle temporal resolution [16][17][18]. The subcycle features in the noise patterns of the generated quantum fields are due to the spatio-temporal modulation of the refractive index of the NX induced by the driving field [18]. This is analogous to a time-dependent metric for the space-time occupied by the electric field, which leads to photon creation in the perspective of a moving observer [19].The spectral properties of ultrabroadband squeezed states are also of particular interest because they can elucidate connections between quantum gravitational effects and their table-top optical analogues. A characteristic example is the Unruh-Davies effect [20,21], according to which an observer in a non-inertial reference frame,

Theory of polaritonic quantum-vacuum detection

“…Following the pioneering works using such setups [7,8,20,22] and the accompanying theoretical analyses [21,[23][24][25], the question regarding the nature of the quantum fluctuations accessed has been raised [26]. In particular, as electro-optic sampling is necessarily carried out inside a nonlinear optical crystal, the relation of the sampled quantum vacuum to the paradigmatic free-space vacuum is an important question.…”

Analysis of Subcycle Electro-Optic Sampling Without Background

“…Recent progress of electro-optic sampling (EOS) in the terahertz (THz) and mid-infrared (MIR) frequency ranges has opened up direct access to the vacuum fluctuations of the electric field [1,2], and routes towards quantum optics operating with subcycle resolution in the time domain are currently being developed [3][4][5]. While cryogenic cooling is required in the THz range to freeze out thermal fluctuations of the field, the quantum limit is reached already at room temperature in the MIR.…”

Determination of the electric field and its Hilbert transform in femtosecond electro-optic sampling

“…Very recently, exploitation of spatiotemporal noise correlations has allowed characterizing the amplitude response of electro-optic detection using either * alfred.leitenstorfer@uni-konstanz.de thermal fields or even the bare vacuum fluctuations as an input [17]. Various prospects for interesting applications of this subcycle quantum technology have been worked out theoretically [18][19][20][21]. These studies include the investigation of traces of ultrashort pulsed squeezed states and their physical implications [18,19], as well as ultrastrong light-matter coupling [20] or manipulation of the electromagnetic groundstate fluctuations through reflecting plates [21].…”

“…Various prospects for interesting applications of this subcycle quantum technology have been worked out theoretically [18][19][20][21]. These studies include the investigation of traces of ultrashort pulsed squeezed states and their physical implications [18,19], as well as ultrastrong light-matter coupling [20] or manipulation of the electromagnetic groundstate fluctuations through reflecting plates [21].…”