Broadband detection of squeezed vacuum: A spectrum of quantum states

Abstract

We demonstrate the simultaneous quantum state reconstruction of the spectral modes of the light field emitted by a continuous wave degenerate optical parametric amplifier. The scheme is based on broadband measurement of the quantum fluctuations of the electric field quadratures and subsequent Fourier decomposition into spectral intervals. Applying the standard reconstruction algorithms to each bandwidth-limited quantum trajectory, a "spectrum" of density matrices and Wigner functions is obtained. The recorded states show a smooth transition from the squeezed vacuum to a vacuum state. In the time domain we evaluated the first order correlation function of the squeezed output field, showing good agreement with theory.The experimental techniques of quantum state reconstruction, first applied five years ago, have opened a new field of research, wherein simple quantum mechanical systems can be characterized completely by density matrices and Wigner functions [1]. Our system consists of electromagnetic field modes at optical frequencies. We have previously generated the whole family of squeezed states of light using an optical parametric amplifier (OPA) and reconstructed these states using the method of optical homodyne tomography [2]. The reconstructions presented therein were limited to essentially one particular pair of modes at frequencies ω ± Ω, where Ω is a radio frequency and ω the optical frequency. The spectral bandwidth of this mode pair was ∆Ω/2π = 100 kHz. Since an OPA pumped below threshold emits a frequency spectrum, with a bandwidth determined by the cavity linewidth in the order of several MHz, the output of the OPA is described more precisely by a whole spectrum of quantum states [3]. General schemes for multimode reconstruction become quite complicated already at the two-mode level [4]. So far only one experiment demonstrating photon-

Squeezed-input, optical-spring, signal-recycled gravitational-wave detectors

“…Squeezed vacuum can be generated with a variable but frequency-independent squeezing angle λ (see for example [39]). A frequency-dependent squeezing angle can be obtained subsequently by filtering the initial squeezed light through detuned FabryPérot (FP) cavities, as proposed by Kimble et al [14], which can rotate the quadratures in a frequency dependent way.…”

Application of quantum inequalities to quantum optics

“…x 0 e −t 2 dt we find R(τ ) = 10 · log[erf(2 √ 2τ )], 9 In the calculation one first splits the expressions into two equal parts and than performs ω → −ω in one of the parts, which after subsequent exchange p ↔ k allows to stretch the ω integration to the whole R. 10 Typically the field is measured on BHD with local oscillator LO [1] (mainly because no device is sensitive enough to measure the vacuum fluctuations directly). The frequency of the LO plus the frequency at which the output of BHD is analyzed give the center ω0 of the sensitivity function µp.…”

“…|f g = d 3 p d 3 k f (p)g(k)a † (p)a † (k)|Ω , where for simplicity the polarization was disregarded. 1 of fields, eg. electromagnetic [9], Dirac [3], even in the situation where the fields propagate in a curved spacetime (which is far more difficult than anything we shall present here).…”

“…In other words the expectation value of the energy density at a point x ̺(x) = : T 00 (x) : S , for certain states |S of the quantum field, can be arbitrarily negative. Let us give a simple example, consider the following state (1) |S = N (|Ω + ǫ|f g ), which is a superposition of the vacuum state |Ω and two particle state |f g 1 . A calculation shows that the energy density, at a certain point x, contains two, generally non-vanishing, terms ̺(x) = ǫA(x) + ǫ 2 B(x), B(x) 0…”

Phase sensitivity of a Mach-Zehnder interferometer with single-intensity and difference-intensity detection

“…Experimental demonstration * stefan.ataman@eli-np.ro † anca.preda10@gmail.com ‡ r.ionicioiu@theory.nipne.ro with a MZI [14] soon followed, proving the usability of the concept in practical measurements. Over the next decades both theoretical and experimental studies have showed how to improve the sensitivity of a MZI fed by both a coherent and a squeezed vacuum input [15][16][17][18]. In a quantum context, however, the phase sensitivity is bounded by the Heisenberg limit [4,11,[19][20][21], ∆ϕ HL ∼ 1/ N , and this limit is fundamental [22].…”