We show that by injecting a light pulse prepared in a non-Gaussian quantum state into the dark port of a two-arm interferometer, it is possible to detect a given phase shift with the fidelity which is limited only by the optical losses and the photodetection inefficiency. The value of the phase shift is inversely proportional to the amplitude of the classical carrier light injected into another (bright) port of the interferometer. It can be reduced by using an additional degenerate parametric amplifier (squeezer) in the input dark port and the matching anti-squeezer in the output dark port. We show that using the modern high-efficiency photon number resolving detectors, it is possible to reduce the detection error by almost one order of magnitude in comparison with the ordinary (Gaussian-state) interferometry.
We show that by injecting a light pulse prepared in a non-Gaussian quantum state into the dark port of a two-arm interferometer, it is possible to detect a given phase shift with the fidelity which is limited only by the optical losses and the photodetection inefficiency. The value of the phase shift is inversely proportional to the amplitude of the classical carrier light injected into another (bright) port of the interferometer. It can be reduced by using an additional degenerate parametric amplifier (squeezer) in the input dark port and the matching anti-squeezer in the output dark port. We show that using the modern high-efficiency photon number resolving detectors, it is possible to reduce the detection error by almost one order of magnitude in comparison with the ordinary (Gaussian-state) interferometry.
It is known that non-Gaussian and only non-Gaussian quantum states can be orthogonal to other quantum states. We show here that, due to this feature, using the non-Gaussian (Fock or Schrödinger cat) states of the probing light, it is possible to detect a given phase shift in optical interferometers with vanishing error probability. Squeezing of the probing non-Gaussian quantum state at the input of the interferometer and the proportional anti-squeezing at the output state allow for the improvement of the sensitivity proportionally to the squeeze factor. The optical losses, most notably the non-ideal quantum efficiency of the photodetection, degrade the sensitivity, introducing finite “false positive” and “false negative” detection errors. However, using state-of-the-art photon-number-resolving detectors, it is still possible to obtain smaller detection error probabilities than in the case of Gaussian quantum states.
Abstract We show that injecting a light pulse prepared in the Shrödinger cat quantum state into the dark port of a two-arm interferometer, it is possible to detect a given phase shift unambiguously. The value of this phase shift is inversely proportional to the amplitudes of both the classical carrier light and the Shrödinger cat state. However, an unconventional detection procedure is required for this purpose. By measuring the number of photons at the output dark port, it is possible to detect the phase shift with a vanishing ‘false positive’ probability. The ‘false negative’ probability in this case decreases as the amplitude of the Schrödinger cat state increases and, for reasonable values of this amplitude, can be made less than about 0.1.
It is shown that the maximal phase sensitivity of a two-path interferometer with high-intensity coherent light and squeezed vacuum in the input ports can be achieved by photon-number-resolving detection of only a small number of photons in a dark output port. It is then possible to achieve the quantum Cram\'er-Rao bound of the two-path interferometer using only the field displacement dependence of the photon number statistics in the single mode output of the dark port represented by a field-displaced squeezed vacuum state. We find that, at small field displacements, it is not sufficient to use the average photon number as the estimator, indicating that an optimal phase estimation depends critically on measurements of the precise photon number. We therefore analyze the effect of detection efficiency on the Fisher information and show that there is a transition from low robustness against photon losses associated with quantum interference effects at low field displacements to high robustness against photon losses at high field displacements. The transition between the two regimes occurs at field shifts proportional to the third power of the squeezing factor, indicating that squeezing greatly enhances the phase interval in which quantum effects are relevant in optimal phase estimations using photon resolving detectors. The case under study could thus be understood as a ``missing link'' between genuine multiphoton interference and the straightforward suppression of noise usually associated with squeezed light.
An important part of optical sensing is interferometry, where direct or homodyne detection at the output of an interferometer yields information about small phase shifts. Classical interferometry operates at the shot-noise limit (SNL), caused by the photon structure of light and reached when an interferometer is fed with coherent light. The use of nonclassical light at the input of an interferometer enables overcoming the SNL. In particular, squeezed light is known to be less noisy than coherent light. An interferometer fed with strongly squeezed light can, in principle, provide the phase sensitivity at the Heisenberg limit, the ultimate limit allowed by the laws of physics. However, this supersensitive operation is strongly degraded by loss – both inside the interferometer and outside it, at the stage of detection. While the former (internal loss) seems to be inevitable, the latter (detection loss) can be overcome, and we demonstrate it in our recent experiment. The clue is to amplify light at the interferometer output using a phase-sensitive optical parametric amplifier. This device does not introduce additional noise, but it amplifies the fragile quantum signal and thus makes it tolerant to loss at the detection stage. In a proof-of-principle experiment, we build a polarization Mach-Zehnder interferometer and feed it with coherent light in one port and a squeezed vacuum in another port. At one output port, we amplify light with an optical parametric amplifier and measure a phase sensitivity of 13 mrad for 1500 photons in the interferometer. This result, achieved with 50% detection efficiency, overcomes the SNL by 3 dB. Moreover, by using stronger amplification, we can overcome the SNL under detection efficiency as low as 13%. Our results outline a way to use squeezed light for real-life sensing, where the detection efficiency cannot be very high, especially in spectral ranges like middle-infrared or terahertz.
In a conventional interferometer one shines light only into one interferometer input port while the second input port is unexcited. This allows vacuum states to enter the unexcited port, leading to imperfect correlation between both the amplitude and the phase fluctuations of the light in the upper and lower interferometer arms. This, in turn, limits the interferometer sensitivity regardless of its operating panel (its arm-length difference, which we in the following will translate into a phase shift θ). The sensitivity of an ideal conventional interferometer is 1 / N. That is, a phase shift of 1 / N radians can be detected with a signal-to-noise ratio of unity by using N photons. Since N typically is a large number, it is tempting to try to find some scheme approaching the fundamental (Heisenberg) limit of phase-shift detection, 1/N. One way of doing that is to inject squeezed vacuum into the unexcited input port of the interferometer.1
We propose to use the antisqueezing-enhanced non-Gaussian Schrödinger cat quantum states of the probing light for the task of detection of a given phase shift in optical interferometers. We show that the antisqueezing allows to increase the robustness of the setup to optical losses. We find the optimal degrees of the antisqueezing for experimentally achievable values of the Schrödinger cat amplitude and the optical losses and compare the resulting sensitivity with the one provided by the Gaussian squeezed states.