Nano-displacement measurements using spatially multimode squeezed light

Abstract

We demonstrate the possibility of surpassing the quantum noise limit for simultaneous multi-axis spatial displacement measurements that have zero mean values. The requisite resources for these measurements are squeezed light beams with exotic transverse mode profiles. We show that, in principle, lossless combination of these modes can be achieved using the non-degenerate Gouy phase shift of optical resonators. When the combined squeezed beams are measured with quadrant detectors, we experimentally demonstrate a simultaneous reduction in the transverse x-and ydisplacement fluctuations of 2.2 dB and 3.1 dB below the quantum noise limit.

Continuous-variable spatial entanglement for bright optical beams

“…Our scheme to produce x-p entanglement between two CW TEM 00 optical beams is shown in Figure 2 and (b) are generated via the in-phase combination of a vacuum squeezed TEM 10 beam with a coherent TEM 00 beam. Such beam combination can be achieved experimentally, for example using an optical cavity or a beamsplitter [21]. The result of the combination is a position squeezed beam.…”

“…This coupled power interferes with the TEM 10 local oscillator beam, causing a change in photo-current observed at the output of the homodyne detector. Thus the difference photo-current of the TEM 10 homodyne detector is given by [17] (21) where N LO and N are the total number of photons in the local oscillator and displaced beams, respectively, with N LO ≫ N . The linearised approximation is utilised, where second order terms in δâ are neglected since N ≫ | δâ 2 n | for all n. In order to measure momentum, one could use a lens to Fourier transform to the far-field plane, where the beam is then measured using the TEM 10 homodyning scheme.…”

Fundamentals and Applications of Quantum Limited Optical Imaging

“…Therefore, two spatial squeezed modes are required to achieve sub-QNL measurements along two different axes in the transverse plane. An experimental demonstration of simultaneous squeezing for quadrant detection along two different axes in the transverse plane was shown by Treps et al (2003). In their experiment, three beams were required -a bright coherent field with a horizontally phase flipped mode-shape, denoted by TEM f 00 , and two squeezed fields with TEM 00 and TEM f 0f 0 (i.e.…”

“…Correspondingly, the beam position fluctuation in the vertical axis were obtained from the difference of the photocurrents from the top and bottom halves of the detector. Treps et al (Treps et al, 2003) demonstrated that simultaneous sub-QNL fluctuations in both horizontal and vertical beam position are obtainable. Treps et al (2002), with permission.…”

Higher-Order Amplitude Squeezing in Six-Wave Mixing Process

“…Jawahar and Jaiswal [6] extended the results obtained by Zhan for amplitudecubed squeezing in the fundamental mode during second and third harmonic generations to kth order. The significant experimental observations include gravity wave detection [7][8][9][10], in optical communication [11], in nanodisplacement measurement [12], and in optical storage [13], and interferometer enhancement [14,15]. The experimental detections and applications confirm the importance of the theoretical investigations into various optical processes such as four-and six-wave mixing [16][17][18][19][20], eight-wave mixing [21], higher-order harmonic generation [22][23][24][25], parametric amplification [26], Raman [27] and hyper-Raman processes [28], and so forth.…”