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Physical Review Letters

Ultrasensitive Two-Mode Interferometry with Single-Mode Number Squeezing

Luca Pezzè, Augusto Smerzi

Published Apr 16, 2013• 132 citations
Publisher

Abstract

A major challenge of the phase estimation problem is the engineering of high-intensity entangled probe states. The goal is to significantly enhance above the shot-noise limit the sensitivity of two-mode interferometers. Here we show that this can be achieved by squeezing in input, and then measuring in output, the population fluctuations of a single mode. The second input mode can be left as an arbitrary nonvacuum (e.g., a bright coherent) state. This two-mode state belongs to a novel class of particle-entangled states which are not spin squeezed. Already a 2.4 db gain above shot noise can be obtained when just a single-particle Fock state is injected into the empty input port of a classical interferometer configuration. Higher gains, up to the Heisenberg limit, can be reached with squeezed states of a larger number of particles. We finally study the robustness of this protocol with respect to detection noise.

DOI
10.1103/physrevlett.110.163604

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A major challenge of the phase estimation problem is the engineering of high-intensity entangled probe states. The goal is to significantly enhance above the shot-noise limit the sensitivity of two-mode interferometers. Here we show that this can be achieved by squeezing in input, and then measuring in output, the population fluctuations of a single mode. The second input mode can be left as an arbitrary nonvacuum (e.g., a bright coherent) state. This two-mode state belongs to a novel class of particle-entangled states which are not spin squeezed. Already a 2.4 db gain above shot noise can be obtained when just a single-particle Fock state is injected into the empty input port of a classical interferometer configuration. Higher gains, up to the Heisenberg limit, can be reached with squeezed states of a larger number of particles. We finally study the robustness of this protocol with respect to detection noise.
We study in detail a system of two interferometers aimed at detecting extremely faint phase fluctuations. This system can represent a breakthrough for detecting a faint correlated signal that would remain otherwise undetectable even using the most sensitive individual interferometric devices, as in the case of so-called holographic noise. The signature of this kind of noise emerges as a correlation between the output signals of the interferometers. On the other hand, when holographic noise is absent one expects uncorrelated signals since the time-averaged fluctuations due to shot noise and other independent contributions vanish (though limiting the overall sensitivity). We show how injecting quantum light in the free ports of the interferometers can reduce the photon noise of the system beyond the shot noise, enhancing the resolution in the phase-correlation estimation. We analyze the use of both the two-mode squeezed vacuum and two independent squeezed states. Our results confirm the benefit of using squeezed beams together with strong coherent beams in interferometry. We also investigate the possible use of the two-mode squeezed vacuum, discovering interesting and unexplored areas of application of bipartite entanglement, in particular the possibility of reaching in principle a surprising uncertainty reduction.
Compared to classical state inputs, using quantum states in interferometers, especially squeezed states, can greatly improve the accuracy of the phase estimation. Here, we propose a scheme based on a Mach-Zehnder interferometer with a displaced two-mode squeezed coherent state input. The scheme employs both intensity difference detection and balanced homodyne detection to achieve high phase sensitivity. The displaced squeezed state exhibits higher accuracy and better robustness by theoretical calculations. For the state, the phase sensitivity of the quantum Cramér-Rao bound and intensity difference detection both exceed the shot noise limit. Additionally, we demonstrate that the proposed state is superior to the two-mode squeezed coherent state by analyzing different displacement operations. Under the presence of both the interferometric transmission loss and the detection loss, higher displacement strength yields higher robustness. To the best of our knowledge, our work provides new ideas for the field of precision measurement.
We provide general bounds of phase estimation sensitivity in linear two-mode interferometers. We consider probe states with a fluctuating total number of particles. With incoherent mixtures of states with different total number of particles, particle entanglement is necessary but not sufficient to overcome the shot noise limit. The highest possible phase estimation sensitivity, the Heisenberg limit, is established under general unbiased properties of the estimator. If coherences can be created, manipulated, and detected, the Heisenberg limit can only be set in the central limit, with a sufficiently large repetition of interferometric measurements.
We consider an optical interferometer with coherent light in one input and a squeezed vacuum in another. Such an interferometer is known to beat the standard quantum limit of sensitivity to the difference of phase shifts in its arms. We find the ultimate limit of precision for such an interferometer by calculating the quantum Fisher information of the mixed quantum state in one of the interferometer's outputs about the difference phase. We show that, in the vicinity of the black fringe, this information is asymptotically close to the quantum Fisher information about this phase for the two-mode readout. We conclude that the single-mode readout is optimal for phase estimation in squeezing-enhanced interferometry and allows for the Heisenberg scaling of precision. We also show that the optimal local measurement in the vicinity of the black fringe consists of amplifying the output field in a phase-sensitive way and measuring its photon number.
We present in this paper a new scheme for optical interferometry. We utilize coherent-beam-stimulated two-mode squeezed light, which interacts with a phase shifter and is then squeezed again before detection. Our theoretical device has the potential to reach far below the shot-noise limit in phase sensitivity. This new proposal avoids the pitfalls of other setups, such as difficulty in creating the required resource. Furthermore, our scheme requires no complicated detection protocol, relying instead only on simple intensity measurement. Also, bright, coherent sources 'boost' squeezed light, creating a very sensitive device. This hybrid scheme relies on no unknown components and can be constructed with current technology. In this paper, we present our analysis of this relatively straightforward device, using the operator propagation method. We derive the phase sensitivity and provide a simple numerical example of the power of our new proposal. Sensitivity to unknown phase shifts scales as a shot-noise-limited Mach–Zehnder interferometer, multiplied by a sub-Heisenberg contribution from the squeezed light.