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Register a new userQuantum Metrology with Two-Mode Squeezed Vacuum: Parity Detection Beats the Heisenberg Limit
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We study the sensitivity and resolution of phase measurement in a Mach-Zehnder interferometer with two-mode squeezed vacuum (<n> photons on average). We show that super-resolution and sub-Heisenberg sensitivity is obtained with parity detection. In particular, in our setup, dependence of the signal on the phase evolves <n> times faster than in traditional schemes, and uncertainty in the phase estimation is better than 1/<n>.
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The interference between coherent and squeezed vacuum light can produce path entangled states with very high fidelities. We show that the phase sensitivity of the above interferometric scheme with parity detection saturates the quantum Cramer-Rao bound, which reaches the Heisenberg-limit when the coherent and squeezed vacuum light are mixed in roughly equal proportions. For the same interferometric scheme, we draw a detailed comparison between parity detection and a symmetric-logarithmic-derivative-based detection scheme suggested by Ono and Hofmann.
We report on an orbital-angular-momentum-enhanced scheme for angular displacement estimation based on two-mode squeezed vacuum and parity detection. The sub-Heisenberg-limited sensitivity for angular displacement estimation is obtained in an ideal situation. Several realistic factors are also considered, including photon loss, dark counts, response-time delay, and thermal photon noise. Our results indicate that the effects of the realistic factors on the sensitivity can be offset by raising orbital angular momentum quantum number $ell$. This reflects that the robustness and the practicability of the system can be improved via raising $ell$ without changing mean photon number $N$.
A recently proposed phase-estimation protocol that is based on measuring the parity of a two-mode squeezed-vacuum state at the output of a Mach-Zehnder interferometer shows that Cram{e}r-Rao bound sensitivity can be obtained [P. M. Anisimov, et al., Phys. Rev. Lett. {bf104}, 103602 (2010)]. This sensitivity, however, is expected in the case of an infinite number of parity measurements made on an infinite number of photons. Here we consider the case of a finite number of parity measurements and a finite number of photons, implemented with photon-number-resolving detectors. We use Bayesian analysis to characterize the sensitivity of the phase estimation in this scheme. We have found that our phase estimation becomes biased near 0 or $pi/2$ phase values. Yet there is an in-between region where the bias becomes negligible. In this region, our phase estimation scheme saturates the Cram{e}r-Rao bound and beats the shot-noise limit.
A proposed phase-estimation protocol based on measuring the parity of a two-mode squeezed-vacuum state at the output of a Mach-Zehnder interferometer shows that the Cram{e}r-Rao sensitivity is sub-Heisenberg [Phys. Rev. Lett. {bf104}, 103602 (2010)]. However, these measurements are problematic, making it unclear if this sensitivity can be obtained with a finite number of measurements. This sensitivity is only for phase near zero, and in this region there is a problem with ambiguity because measurements cannot distinguish the sign of the phase. Here, we consider a finite number of parity measurements, and show that an adaptive technique gives a highly accurate phase estimate regardless of the phase. We show that the Heisenberg limit is reachable, where the number of trials needed for mean photon number $bar{n}=1$ is approximately one hundred. We show that the Cram{e}r-Rao sensitivity can be achieved approximately, and the estimation is unambiguous in the interval ($-pi/2, pi/2$).
Two-mode interferometers, such as Michelson interferometer based on two spatial optical modes, lay the foundations for quantum metrology. Instead of exploring quantum entanglement in the two-mode interferometers, a single bosonic mode also promises a measurement precision beyond the shot-noise limit (SNL) by taking advantage of the infinite-dimensional Hilbert space of Fock states. However, the experimental demonstration still remains elusive. Here, we demonstrate a single-mode phase estimation that approaches the Heisenberg limit (HL) unconditionally. Due to the strong dispersive nonlinearity and long coherence time of a microwave cavity, quantum states of the form $left(left|0rightrangle +left|Nrightrangle right)/sqrt{2}$ are generated, manipulated and detected with high fidelities, leading to an experimental phase estimation precision scaling as $sim N^{-0.94}$. A $9.1$~$mathrm{dB}$ enhancement of the precision over the SNL at $N=12$, which is only $1.7$~$mathrm{dB}$ away from the HL, is achieved. Our experimental architecture is hardware efficient and can be combined with the quantum error correction techniques to fight against decoherence, thus promises the quantum enhanced sensing in practical applications.
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