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

T. L. M. Guedes, M. Kizmann, D. V. Seletskiy, A. Leitenstorfer, Guido Burkard, and A. S. Moskalenko

Phys. Rev. Lett. 122, 053604 – Published 8 February 2019

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 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. They 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.

Received 18 October 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.053604

Physics Subject Headings (PhySH)

Optical tests of quantum theory Photon pairs & parametric down-conversion Squeezing of quantum noise Ultrafast phenomena Unruh effect

General PhysicsGravitation, Cosmology & AstrophysicsQuantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

T. L. M. Guedes^1,*, M. Kizmann¹, D. V. Seletskiy^1,2, A. Leitenstorfer¹, Guido Burkard¹, and A. S. Moskalenko^1,3,†

¹Department of Physics and Center for Applied Photonics, University of Konstanz, D-78457 Konstanz, Germany
²Department of Engineering Physics, Polytechnique Montréal, Montréal, H3T 1J4, Canada
³Department of Physics, KAIST, Daejeon 34141, Republic of Korea

^*thiago.lucena@uni-konstanz.de
^†andrey.moskalenko@uni-konstanz.de

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 122, Iss. 5 — 8 February 2019

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) General sketch of the proposed experimental setup. The classical driving field propagates through a $χ^{(2)}$ nonlinear crystal (NX) of small thickness $L$ and unperturbed refractive index $n$ , generating ultrabroadband squeezed quantum light. The outgoing light is registered by the detector $D$ . (b) World line of a plane wave mode of the quantum electric field within the NX with refractive index modulated by a half-cycle pulse (HCP). The trajectory (blue line) is given by Eq. (9) with $C_{1} = 0$ , $α / n^{2} = 0.49$ , and $n ζ = 12$ . The dotted purple straight line indicates the trajectory of light in the absence of nonlinear effects. After the acceleration has mostly ceased, the world line approaches the dotted green line parallel to the purple one. The process of acceleration is confined to a diamondlike space-time zone (light red parallelogram) of dimensions defined by the duration of the driving transient.
Reuse & Permissions
Figure 2
(a) Normalized spectral photon flux density in the case of cw driving ( $ρ_{0} = C^{2} | E_{0} |^{2} Γ / π^{2}$ , $Γ = ω_{0}$ for cw). Calculations including up to second-order (blue) and fourth-order (red) terms in $α = d E_{0}$ have been included. The value of the factor $π^{4} ρ_{0} ω_{0} / 4$ governing the smallness of the $α^{4}$ term with respect to the $α^{2}$ term is 0.02. The dotted curve shows the average spectral photon flux density for a measurement over a finite time interval $Δ t = N T$ with $N = 50$ , where $T = 2 π / ω_{0}$ is the period of the driving field. (b) Normalized spectral photon density (SPD) for the driving HCP (dotted blue line) and SCP (solid blue line) cases in the leading ( $α^{2}$ ) order. The exponential behavior of the spectra can be better analyzed in a logarithmic plot, presented for the HCP case in the inset (same high-frequency behavior as for the SCP case). The SPD is shown in blue, while the asymptotic dotted straight line represents a fit of the form $A e^{- π (ω / Γ)}$ .
Reuse & Permissions
Figure 3
Dynamics of the normally ordered variance (NOV), $V (τ)$ , of the emitted quantum electric field for (a) cw, (b) HCP, and (c) SCP driving (dotted green line). Contributions up to the first $V^{(1)} (τ)$ (blue line) and the second $V^{(1)} (τ) + V^{(2)} (τ)$ (red line) order in the squeezing strength $r$ are shown. The NOV is normalized by $V_{0} = ℏ Γ^{2} / (24 π ε_{0} c_{0} n A)$ , while time is normalized by $Γ$ ( $Γ = ω_{0}$ for cw driving). $r = 0.07$ for (a), 0.21 for (b), and 1.54 for (c).
Reuse & Permissions
Figure 4
World lines of the modes of quantum light propagating through the NX for HCP (a) and SCP (b) driving. Each world line (blue) is defined by its initial condition, which is given by a certain event at the boundary of the crystal and correspondingly by the amplitude of the driving field (green line) at this event. Here $α / n^{2} = 0.49$ and $n ζ = 12$ (see Ref. [39]).
Reuse & Permissions

Physical Review Letters