Deterministic Superresolution with Coherent States at the Shot Noise Limit

Abstract

Interference of light fields plays an important role in various high-precision measurement schemes. It has been shown that superresolving phase measurements beyond the standard coherent state limit can be obtained either by using maximally entangled multiparticle states of light or using complex detection approaches. Here we show that superresolving phase measurements at the shot noise limit can be achieved without resorting to nonclassical optical states or to low-efficiency detection processes. Using robust coherent states of light, high-efficiency homodyne detection, and a deterministic binarization processing technique, we show a narrowing of the interference fringes that scales with 1/√[N] where N is the mean number of photons of the coherent state. Experimentally we demonstrate a 12-fold narrowing at the shot noise limit.

Quantum interferometry with binary-outcome measurements in the presence of phase diffusion

“…1). Similar to the experimental setup [15], a coherent state |α with amplitude α = √ N is injected into one port of the MZI and the other port is left in vacuum |0 . After a 50:50 beamsplitter [26,27], the photon state becomes a product of coherent states |α/ √ 2 a ⊗ |α/ √ 2 b , where the subscript a (b) denotes the path or the polarization mode.…”

“…After a 50:50 beamsplitter [26,27], the photon state becomes a product of coherent states |α/ √ 2 a ⊗ |α/ √ 2 b , where the subscript a (b) denotes the path or the polarization mode. Second, the phase shift φ is accumulated in one arm of the interferometer [15] …”

“…Recently, Gao et al [14] proposed that the parity measurement can lead to the super-resolution in the coherentlight MZI. Using a binary-outcome homodyne detection, Distante et al [15] have demonstrated a super-resolution with the FWHM ∼ π/ √ N and a phase sensitivity close to the shotnoise limit. Most recently, Cohen et al [16] have realized the parity measurement in a polarization version of the MZI.…”

“…In this paper, we present a unified description to the above coherent-light MZI experiments [15,16], using general expressions of conditional probabilities for detecting an outcome in homodyne detection and in photon counting measurement. We first show that for a general binary-outcome measurement, the simplest data processing based on inverting the average signal can saturate the Cramér-Rao (CR) bound.…”

Single-photon quantum nonlocality: Violation of the Clauser-Horne-Shimony-Holt inequality using feasible measurement setups

“…We can thus define a homodyne-binning operatorX θ ≡ ( Z+ − Z− )|x θ x θ |dx θ . For pure homodyne measurements, we adopt the center-binning convention [33]. Then a general Gaussian operation shifts, rescales, and rotates the profile.…”