We report an experimental demonstration of optimal measurements of small displacement and tilt of a Gaussian beam - two conjugate variables - involving a homodyne detection with a TEM10 local oscillator. We verify that the standard split detection is only 64% efficient. We also show a displacement measurement beyond the quantum noise limit, using a squeezed vacuum TEM10 mode within the input beam.
In this paper, we study how a displacement of a quantum system appears under a change of relativistic reference frame. We introduce a generic method in which a displacement operator in one reference frame can be transformed into another reference frame. It is found that, when moving between non-inertial reference frames there can be distortions of phase information, modal structure and amplitude. We analyse how these effects affect traditional homodyne detection techniques. We then develop an in principle homodyne detection scheme which is robust to these effect, called the ideal homodyne dete…
We experimentally demonstrate a new measurement scheme for the discrimination of two coherent states. The measurement scheme is based on a displacement operation followed by a photon number resolving detector, and we show that it outperforms the standard homodyne detector which we, in addition, proof to be optimal within all Gaussian operations including conditional dynamics. We also show that the non-Gaussian detector is superior to the homodyne detector in a continuous variable quantum key distribution scheme.
Homodyne and heterodyne detection represent "twin-pillars" of quantum displacement sensing using optical cavities, having permitted major breakthroughs including detection of gravitational waves and of the motion of quantum ground-state cooled mechanical oscillators. Both can suffer disadvantages as diagnostics in quantum optomechanics, either through symmetrisation (homodyne), or loss of correlations (heterodyne). We show that, for modest heterodyne beat frequencies ($Ω\sim ω_M/10 \gg Γ$), judicious construction of the autocorrelation of the measured current can either recover (i) a spectrum …
Optical satellite links open up new prospects for realizing quantum physical experiments over unprecedented length scales. We analyze and affirm the feasibility of detecting quantum squeezing in an optical mode with homodyne detection of only one bit resolution, as is found in satellites already in orbit. We show experimentally that, in combination with a coherent displacement, a binary homodyne detector can still detect quantum squeezing efficiently even under high loss. The sample overhead in comparison to non-discretized homodyne detection is merely a factor of 3.3.
We consider the problem of measurement of optical transverse profile parameters and their conjugate variable. Using multi-mode analysis, we introduce the concept of detection noise-modes. For Gaussian beams, displacement and tilt are a pair of transverse profile conjugate variables. We experimentally demonstrate their optimal encoding and detection with a spatial homodyning scheme. Using higher order spatial mode squeezing, we show the sub-shot noise measurements for the displacement and tilt of a Gaussian beam.
We investigated the estimation of an unknown Gaussian process (containing displacement, squeezing and phase-shift) applied to a matter system. The state of the matter system is not directly measured; instead, we measure an optical mode which interacts with the system. We propose an interferometric setup exploiting a beam-splitter-type of light-matter interaction with homodyne detectors and two methods of estimation. We demonstrate the superiority of the interferometric setup over alternative non-interferometric schemes. Importantly, we show that even limited coupling strength and a noisy matte…
We present a quantum receiver for quadrature amplitude modulation (QAM) coherent states discrimination with homodyne-displacement hybrid structure. Our strategy is to carry out two successive measurements on parts of the quantum states. The homodyne result of the first measurement reveals partial information about the state and is forward to a displacement receiver, which finally identifies the input state by using feedback to adjust a reference field. Numerical simulation results show that for 16-QAM, the hybrid receiver could outperform the standard quantum limit (SQL) with a reduced number …
We experimentally realize a great precision enhancement in the small tilt measurement by using a Sagnac interferometer and balanced homodyne detection (BHD) of high-order optical modes, together with the weak value amplification (WVA) technique. Smaller minimum measurable tilt (MMT) and higher signal-to-noise ratio (SNR) can be obtained by using BHD, compared with the split detection (SD). The precision of 3.8 nrad can be obtained under our present experimental condition. It is shown that combining WVA technique and BHD can strengthen each other's advantages and can behave better for some spec…
We derive the quantum noise limit for the optical beam displacement of a TEM00 mode. Using a multimodal analysis, we show that the conventional split detection scheme for measuring beam displacement is non-optimal with 80% efficiency. We propose a new displacement measurement scheme that is optimal for small beam displacement. This scheme utilises a homodyne detection setup that has a TEM10 mode local oscillator. We show that although the quantum noise limit to displacement measurement can be surpassed using squeezed light in appropriate spatial modes for both schemes, the TEM10 homodyning sch…
We calculate the Holevo Cramér-Rao bound for estimation of the displacement experienced by one mode of an two-mode squeezed vacuum state with squeezing r and find that it is equal to 4exp(-2r). This equals the sum of the mean squared error obtained from a dual homodyne measurement, indicating that the bound is tight and that the dual homodyne measurement is optimal.
Graph states are a unique resource for quantum information processing, such as measurement-based quantum computation. Here, we theoretically investigate using continuous-variable graph states for single-parameter quantum metrology, including both phase and displacement sensing. We identified the optimal graph states for the two sensing modalities and showed that Heisenberg scaling of the accuracy for both phase and displacement sensing can be achieved with local homodyne measurements.
We investigate quantum nonlocality of a single-photon entangled state under feasible measurement techniques consisting of on-off and homodyne detections along with unitary operations of displacement and squeezing. We test for a potential violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality, in which each of the bipartite party has a freedom to choose between 2 measurement settings, each measurement yielding a binary outcome. We find that single-photon quantum nonlocality can be detected when two or less of the 4 total measurements are carried out by homodyne detection. The largest vio…
In this paper, we propose a protocol for angular displacement estimation based upon orbital angular momentum coherent state and a SU(1,1)-SU(2) hybrid interferometer. This interferometer consists of an optical parametric amplifier, a beam splitter and reflection mirrors, hereon we use a quantum detection strategy $\---$ balanced homodyne detection. The results indicate that super-resolution and super-sensitivity can be realized with ideal condition. Additionally, we study the impact of photon loss on the resolution and the sensitivity, and the robustness of our protocol is also discussed. Fina…
A methodology is introduced that enables an absolute, quantum-limited measurement of sub-wavelength interferometric displacements. The technique utilizes a high-frequency optical path modulation within an interferometer operated in a homodyne configuration. All of the information necessary to fully characterize the resultant path displacement is contained within the relative strengths of the various harmonics of the phase modulation. The method, which is straightforward and readily implementable, allows a direct measurement of the theoretical Cramér-Rao limit of detection without any assumptio…
The extraordinary sensitivity of the output field of an optical cavity to small quantum-scale displacements has led to breakthroughs such as the first detection of gravitational waves \cite{LIGO,LIGODC} and of the motions of quantum ground-state cooled mechanical oscillators \cite{Teufel2011,Chan2011}. While heterodyne detection of the cavity field preserves asymmetries which provide a key signature that mechanical oscillators has attained the quantum regime, detection of a rotating quadrature of the light averages out important quantum correlations, yielding a weaker signal and lower sensitiv…
We investigate the capabilities of loss-tolerant quantum state characterization using a photon-number resolving, time-multiplexed detector (TMD). We employ the idea of probing the Wigner function point-by-point in phase space via photon parity measurements and displacement operations, replacing the conventional homodyne tomography. Our emphasis lies on reconstructing the Wigner function of non-Gaussian Fock states with highly negative values in a scheme that is based on a realistic experimental setup. In order to establish the concept of loss-tolerance for state characterization we show how lo…
We investigate interferometric techniques to estimate the deflection angle of an optical beam and compare them to the direct detection of the beam deflection. We show that quantum metrology methods lead to a unifying treatment for both single photons and classical fields. Using the Fisher information to assess the precision limits of the interferometric schemes, we show that the precision can be increased by exploiting the initial transverse displacement of the beam. This gain, which is present for both Sagnac and Mach-Zehnder-like configurations, can be considerable when compared to non-inter…
Nonlinear interferometers that replace beamsplitters in Mach-Zehnder interferometers with nonlinear amplifiers for quantum-enhanced phase measurements have drawn increasing interest in recent years, but practical quantum sensors based on nonlinear interferometry remain an outstanding challenge. Here, we demonstrate the first practical application of nonlinear interferometry by measuring the displacement of an atomic force microscope microcantilever with quantum noise reduction of up to 3~dB below the standard quantum limit, corresponding to a quantum-enhanced measurement of beam displacement o…
We provide the optimal measurement strategy for a class of noisy channels that reduce to the identity channel for a specific value of a parameter (spreading channels). We provide an example that is physically relevant: the estimation of the absolute value of the displacement in the presence of phase randomizing noise. Surprisingly, this noise does not affect the effectiveness of the optimal measurement. We show that, for small displacement, a squeezed vacuum probe field is optimal among strategies with same average energy. A squeezer followed by photodetection is the optimal detection strategy…
We present an interferometric technique for measuring ultra-small tilts. The information of a tilt in one of the mirrors of a modified Sagnac interferometer is carried by the phase difference between the counter propagating laser beams. Using a small misalignment of the interferometer, orthogonal to the plane of the tilt, a bimodal (or two-fringe) pattern is induced in the beam's transverse power distribution. By tracking the mean of such a distribution, using a split detector, a sensitive measurement of the phase is performed. With 1.2 mW of continuous-wave laser power, the technique has a sh…
We present an investigation into the tilt sensitivity of the canonical, optical, weak-value amplification device (COWVAD), introduced by Duck, Stevenson, and Sudarshan in 1989, for potential application in a Coriolis vibratory gyroscope (CVG). We model the breakdown of the weak-value amplification effect in this device with respect to angle of incidence between the laser beam and the surface of the birefringent crystal. Additionally, we model the effect of beam divergence due to misalignment of the crystals optic axis. We found that the presence of beam divergence allows the architecture to be…
Phase Independent Measurement of Weak Coherent Optical Signals
University of Tennessee, Chattanooga（田纳西大学查塔努加分校）；FAMU–FSU College of Engineering, Florida State University（佛罗里达州立大学 FAMU-FSU 工程学院）；Department of Biological and Agricultural Engineering, Texas A&M University（德克萨斯农工大学生物与农业工程系）
We address the joint estimation of the two defining parameters of a displacement operation in phase space. In a measurement scheme based on a Gaussian probe field and two homodyne detectors, it is shown that both conjugated parameters can be measured below the standard quantum limit when the probe field is entangled. We derive the most informative Cramér-Rao bound, providing the theoretical benchmark on the estimation and observe that our scheme is nearly optimal for a wide parameter range characterizing the probe field. We discuss the role of the entanglement as well as the relation between o…
We analyze the amplification by the Aharonov-Albert-Vaidman weak quantum measurement on a Sagnac interferometer [P. B. Dixon et al., Phys. Rev. Lett. 102, 173601 (2009)] up to all orders of the coupling strength between the measured system and the measuring device. The amplifier transforms a small tilt of a mirror into a large transverse displacement of the laser beam. The conventional analysis has shown that the measured value is proportional to the weak value, so that the amplification can be made arbitrarily large in the cost of decreasing output laser intensity. It is shown that the measur…
It is not clear if the performance of a quantum lidar or radar, without an idler and only using Gaussian resources, could exceed the performance of a semiclassical setup based on coherent states and homodyne detection. Here we prove this is indeed the case by showing that an idler-free squeezed-based setup can beat this semiclassical benchmark. More generally, we show that probes whose displacement and squeezing are jointly optimized can strictly outperform coherent states with the same mean number of input photons for both the problems of quantum illumination and reading.
The measurement of weak continuous forces exerted on a mechanical oscillator is a fundamental problem in various physical experiments. It is fundamentally impeded by quantum back-action from the meter used to sense the displacement of the oscillator. In the context of interferometric displacement measurements, we here propose and demonstrate the working principle of a scheme for coherent back-action cancellation. By measuring the amplitude quadrature of the light reflected from a detuned optomechanical cavity inside which a stiff optical spring is generated, back-action can be cancelled in a n…
The central issue in quantum parameter estimation is to find out the optimal measurement setup that leads to the ultimate lower bound of an estimation error. We address here a question of whether a Gaussian measurement scheme can achieve the ultimate bound for phase estimation in single-mode Gaussian metrology that exploits single-mode Gaussian probe states in a Gaussian environment. We identify three types of optimal Gaussian measurement setups yielding the maximal Fisher information depending on displacement, squeezing, and thermalization of the probe state. We show that the homodyne measure…
Estimation of a global parameter defined as a weighted linear combination of unknown multiple parameters can be enhanced by using quantum resources. Advantageous quantum strategies may vary depending on the weight distribution, requiring the study of optimal schemes achieving a maximal quantum advantage for a given sensing scenarios. In this work, we propose an optimal distributed quantum phase sensing scheme using Gaussian states with zero displacement for an arbitrary distribution of the weights with positive and negative signs. The estimation precision of the optimal scheme is derived, and …
We investigate quantum teleportation of ensembles of coherent states of light with a Gaussian distributed displacement in phase space. Recently, the following general question has been addressed in [P. Liuzzo-Scorpo et al., arXiv:1705.03017]: Given a limited amount of entanglement and mean energy available as resources, what is the maximal fidelity that can be achieved on average in the teleportation of such an alphabet of states? Here, we consider a variation of this question, where Einstein-Podolsky-Rosen steering is used as a resource rather than plain entanglement. We provide a solution by…
