Approaching the Heisenberg limit with two-mode squeezed states

Abstract

Two mode squeezed states can be used to achieve Heisenberg limit scaling in interferometry: a phase shift of δϕ ≈ 2.76/ N can be resolved. The proposed scheme relies on balanced homodyne detection and can be implemented with current technology. The most important experimental imperfections are studied and their impact quantified.PACS numbers: 42.50. Dv, 42.87.Bg, 03.75.Dg The best possible phase resolution for an interferometer is given by the Heisenberg limit for the minimum detectable phase shift δϕ = 1/ N ; here N is the average intensity (number of photons or other bosons). Present optical interferometers typically operate at the shot noise resolution limit δϕ ∼ 1/ N . Interest in reaching the Heisenberg-limit is great because it presents a fundamental limit and overcomes the shot-noise limit leading to potential applications in high resolution distance measurements, for instance, to detect gravitational waves [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17].Known, feasible schemes use degenerate squeezed vacuum combined with Glauber-coherent light to increase the phase sensitivity achieving sub-shot noise resolution, but do not reach the Heisenberg limit [6,7]. Indeed, no practical scheme has been found that shows scaling like the Heisenberg limit δϕ = κ/ N for large intensities (and preferably a small constant κ).More recent publications describing schemes that theoretically reach the Heisenberg limit have mostly considered quantum states which are very hard to synthesize [8,9,10,12,13,15,16,17] and suggest to use unrealistically high non-linearities to guide the light through the interferometer [10] or detectors which have single photon resolution even when dealing with very many photons [4,5,8,9,12,13,14,15,16,17].This Letter proposes to use a standard linear twopath interferometer fed with two mode squeezed vacuum states degenerate in energy and polarization [5,9], see FIG. 1. But rather than measuring photon numbers (intensities) we want to measure the product of the output ports' quadrature components, i.e. perform balanced homodyne detection [1,18]. The only non-linearities used in the setup proposed here are those of the crystal for parametric down-conversion to generate the two mode squeezed vacuum state. It turns out that modest squeezing, i.e. low intensities, suffice to reach interferometric resolution at approximately three times the Heisenberg limit The use of balanced homodyne detection removes the detection problems mentioned above. Because only well established technology is required [18,19,20] a proof-ofprinciple experiment will be immediately possible.In order to derive our main result (1) we follow the conventions of reference [21]: In the Heisenberg picture the action of the parametric amplifier is described by photon operator transformationsâ 1 = Uâ 0 + Vb † 0 andb 1 = Ub 0 + Vâ † 0 where U = cosh G and V = −i exp(iξ) sinh G with the single pass gain G = g|E p |L and a relative phase ξ which we will assume to be zero. L is the interaction path length, E p the pump laser's amplitude, and ...

The phase sensitivity of an SU(1,1) interferometer with coherent and squeezed-vacuum light

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Effects of losses in the atom-light hybrid SU(1,1) interferometer

“…In current optical measurement of phase sensitivity, the homodyne detection [54][55][56] and the intensity detection [32,35] are often used. That is, the observables are the amplitude quadrature operatorx a2 = (â 2 +â † 2 )/2 and the number operatorn a2 =â † 2â 2 .…”

Sensing performance enhancement via asymmetric gain optimization in the atom-light hybrid interferometer

“…Interferometers are widely used as sensors in precision measurement [1][2][3][4]. There have been many kinds of interferometers, such as optical interferometers [5][6][7], atom interferometers [8][9][10][11][12][13] and atom-light hybrid interferometer (ALHI) [14,15]. Optical interferometers can measure the optical phase sensitive quantitation and are the core of optical gyroscopes [16], laser radar [17], ranging systems [18], etc.…”