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Register a new userCoherent and Squeezed Vacuum Light Interferometry: Parity detection hits the Heisenberg limit
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Added by
Kaushik Seshadreesan
Publication date
2011
fields
Physics
and research's language is
English
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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.
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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>.
Two path interferometry with coherent states and squeezed vacuum can achieve phase sensitivities close to the Heisenberg limit when the average photon number of the squeezed vacuum is close to the average photon number of the coherent light. Here, we investigate the phase sensitivity of such states in the presence of photon losses. It is shown that the Cramer-Rao bound of phase sensitivity can be achieved experimentally by using a weak local oscillator and photon counting in the output. The phase sensitivity is then given by the Fisher information F of the state. In the limit of high squeezing, the ratio (F-N)/N^2 of Fisher information above shot noise to the square of the average photon number N depends only on the average number of photons lost, n_loss, and the fraction of squeezed vacuum photons mu. For mu=1/2, the effect of losses is given by (F-N)/N^2=1/(1+2 n_loss). The possibility of increasing the robustness against losses by lowering the squeezing fraction mu is considered and an optimized result is derived. However, the improvements are rather small, with a maximal improvement by a factor of two at high losses.
Entangled coherent states are shown to emerge, with high fidelity, when mixing coherent and squeezed vacuum states of light on a beam-splitter. These maximally entangled states, where photons bunch at the exit of a beamsplitter, are measured experimentally by Fock-state projections. Entanglement is examined theoretically using a Bell-type nonlocality test and compared with ideal entangled coherent states. We experimentally show nearly perfect similarity with entangled coherent states for an optimal ratio of coherent and squeezed vacuum light. In our scheme, entangled coherent states are generated deterministically with small amplitudes, which could be beneficial, for example, in deterministic distribution of entanglement over long distances.
We investigate the prospect of enhancing the phase sensitivity of atom interferometers in the Mach-Zehnder configuration with squeezed light. Ultimately, this enhancement is achieved by transferring the quantum state of squeezed light to one or more of the atomic input beams, thereby allowing operation below the standard quantum limit. We analyze in detail three specific schemes that utilize (1) single-mode squeezed optical vacuum (i.e. low frequency squeezing), (2) two-mode squeezed optical vacuum (i.e. high frequency squeezing) transferred to both atomic inputs, and (3) two-mode squeezed optical vacuum transferred to a single atomic input. Crucially, our analysis considers incomplete quantum state transfer (QST) between the optical and atomic modes, and the effects of depleting the initially-prepared atomic source. Unsurprisingly, incomplete QST degrades the sensitivity in all three schemes. We show that by measuring the transmitted photons and using information recycling [Phys. Rev. Lett. 110, 053002 (2013)], the degrading effects of incomplete QST on the sensitivity can be substantially reduced. In particular, information recycling allows scheme (2) to operate at the Heisenberg limit irrespective of the QST efficiency, even when depletion is significant. Although we concentrate on Bose-condensed atomic systems, our scheme is equally applicable to ultracold thermal vapors.
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 $N$.
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