我们设计并通过实验演示了一种硅光子集成的时域平衡零差探测器（TBHD），其光学部分尺寸为1.5 mm × 0.4 mm。为了自动且精确地平衡该探测器，我们采用了新型可调光衰减器，可实现86.9 dB的共模抑制比。在量子层析实验中，以99.97%的保真度重构了相干态的密度矩阵和Wigner函数。我们还演示了该TBHD在连续变量量子密钥分发（CVQKD）系统中的可行性。这有助于利用TBHD将基于GG02协议的CVQKD系统的光学光路集成到硅光子芯片上。
英文摘要：
We designed and experimentally demonstrated a silicon photonics-integrated time-domain balanced homodyne detector (TBHD), whose optical part has dimensions of 1.5 mm * 0.4 mm. To automatically and accurately balance the detector, new variable optical attenuators were used, and a common mode rejection ratio of 86.9 dB could be achieved. In the quantum tomography experiment, the density matrix and Wigner function of a coherent state were reconstructed with 99.97 % fidelity. The feasibility of this TBHD in a continuous-variable quantum key distribution (CVQKD) system was also demonstrated. This facilitates the integration of the optical circuits of the CVQKD system based on the GG02 protocol on the silicon photonics chip using TBHD.
We demonstrate a die-level balanced homodyne detector with a high quantum-to-classical noise clearance of 19.1dB over 3GHz bandwidth. We evaluate this receiver as a high-quality entropy source for random number generation at >10Gb/s and prove the functional integration of a classical 10Gb/s duobinary communication channel.
We discuss excess noise contributions of a practical balanced homodyne detector in Gaussian-modulated coherent-state (GMCS) quantum key distribution (QKD). We point out the key generated from the original realistic model of GMCS QKD may not be secure. In our refined realistic model, we take into account excess noise due to the finite bandwidth of the homodyne detector and the fluctuation of the local oscillator. A high speed balanced homodyne detector suitable for GMCS QKD in the telecommunication wavelength region is built and experimentally tested. The 3dB bandwidth of the balanced homodyne …
In this paper we investigate the security of a quantum cryptographic scheme which utilizes balanced homodyne detection and weak coherent pulse (WCP). The performance of the system is mainly characterized by the intensity of the WCP and postselected threshold. Two of the simplest intercept/resend eavesdropping attacks are analyzed. The secure key gain for a given loss is also discussed in terms of the pulse intensity and threshold.
We report an experimental quantum key distribution that utilizes balanced homodyne detection, instead of photon counting, to detect weak pulses of coherent light. Although our scheme inherently has a finite error rate, it allows high-efficiency detection and quantum state measurement of the transmitted light using only conventional devices at room temperature. When the average photon number was 0.1, an error rate of 0.08 and "effective" quantum efficiency of 0.76 were obtained.
We present the characterization of a novel balanced homodyne detector operating in the mid-infrared. The challenging task of revealing non-classicality in mid-infrared light, e.~g. in quantum cascade lasers emission, requires a high-performance detection system. Through the intensity noise power spectral density analysis of the differential signal coming from the incident radiation, we show that our setup is shot-noise limited. We discuss the experimental results with a view to possible applications to quantum technologies, such as free-space quantum communication.
Low-noise, efficient, phase-sensitive time-domain optical detection is essential for foundational tests of quantum physics based on optical quantum states and the realization of numerous applications ranging from quantum key distribution to coherent classical telecommunications. Stability, bandwidth, efficiency, and signal-to-noise ratio are crucial performance parameters for effective detector operation. Here we present a high-bandwidth, low-noise, ultra-stable time-domain coherent measurement scheme based on balanced homodyne detection ideally suited to characterization of quantum and classi…
A simple scheme for conditional generation of nonclassical light with sub-Poissonian photon-number statistics is proposed. The method utilizes entanglement of signal and idler modes in two-mode squeezed vacuum state generated in optical parametric amplifier. A quadrature component of the idler mode is measured in balanced homodyne detector and only those experimental runs where the absolute value of the measured quadrature is higher than certain threshold are accepted. If the threshold is large enough then the conditional output state of signal mode exhibits reduction of photon-number fluctuat…
We consider the moment operators of the observable (i.e. a semispectral measure or POM) associated with the balanced homodyne detection statistics, with paying attention to the correct domains of these unbounded operators. We show that the high amplitude limit, when performed on the moment operators, actually determines uniquely the entire statistics of a rotated quadrature amplitude of the signal field, thereby verifying the usual assumption that the homodyne detection achieves a measurement of that observable. We also consider, in a general setting, the possibility of constructing a measurem…
A pulsed balanced homodyne detector has been developed for precise measurements of electric field quadratures of pulsed optical quantum states. A high level of common mode suppression (> 85 dB) and low electronic noise (730 electrons per pulse) provide a signal to noise ratio of 14 dB for the measurement of the quantum noise of individual pulses. Measurements at repetition rates up to 1 MHz are possible. As a test, quantum tomography of the coherent state is performed and the Wigner function and the density matrix are reconstructed with a 99.5% fidelity. The detection system can also be used f…
Driven by single photon detection requirements especially for quantum information sciences, the theory of arrays of off-on detectors has been well developed and applied. However for a comprehensive characterization of nonclassicality one also needs phase sensitive properties. This missing link is fulfilled by the theory of phase sensitive click counting measurements. This theory is presented. It unifies the balanced homodyne detection for high intensities with the click detection in the few photon regime. We formulate and apply a hierarchy of nonlinear squeezing conditions to probe quantum eff…
Within the dipole approximation we describe the interaction of a photodiode with the quantum electric field. The diode is modelled by an electron in a bound state which upon interaction, treated perturbatively in the paper, can get excited to one of the scattering states. We furthermore analyze a balanced homodyne detector (BHD) with a local oscillator (LO) consisting of two photodiodes illuminated by a monochromatic coherent state. We show, that to the leading order the BHD's output measures the expectation value of the quantum electric field, in the state without the LO, restricted to the fr…
In the context of the readout scheme for gravitational-wave detectors, the "double balanced homodyne detection" proposed in [K.~Nakamura and M.-K.~Fujimoto, arXiv:1709.01697.] is discussed in detail. This double balanced homodyne detection enables us to measure the expectation values of the photon creation and annihilation operators. Although it has been said that the operator $\hat{b}_θ:=\cosθ\hat{b}_{1}+\sinθ\hat{b}_{2}$ can be measured through the homodyne detection in literature, we first show that the expectation value of the operator $\hat{b}_θ$ cannot be measured as the linear combinati…
We recall and generalize the analysis of the output of the so-called balanced homodyne detectors. The most important feature of these detectors is their ability to quantify the vacuum fluctuations of the electric field, that is expectation values of products of (quantum-) electric-field operators. More precisely, the output of BHDs provides information on the one- and two-point functions of arbitrary states of quantum fields. We generalize the analysis of the response of BHDs to the case of quantum fields under influence of static external conditions such as cavities or polarizable media. By r…
A measurement technique is proposed which, in principle, allows one to observe the general space-time correlation properties of a quantized radiation field. Our method, called balanced homodyne correlation measurement, unifies the advantages of balanced homodyne detection with those of homodyne correlation measurements.
We experimentally study optical homodyne and heterodyne detections with a same setup, which is flexible to manipulate the signal sideband modulation. When the modulation only generate a single signal sideband, the light field measurement by mixing the single sideband at $ω_{0}+Ω$ with a strong local oscillator at the carrier frequency $ω_{0}$ on a beam splitter become balanced heterodyne detection. When two signal sidebands at $ω_{0}\pmΩ$ are generated and the relative phase of the two sidebands is locked, this measurement corresponds to optical balanced homodyne detection. With this setup, we…
The balanced homodyne detection as a readout scheme of gravitational-wave detectors is carefully examined, which specifies the directly measured quantum operator in the detection. This specification is necessary to apply the quantum measurement theory to gravitational-wave detections. We clarify the contribution of vacuum fluctuations to the noise spectral density without using the two-photon formulation. We found that the noise spectral density in the two-photon formulation includes vacuum fluctuations from the main interferometer but does not includes those from the local oscillator which de…
Traditional method for measuring continuous-variable quantum entanglement relies on balanced homodyne detections, which are sensitive to vacuum quantum noise coupled in through losses resulted from many factors such as detector's quantum efficiency and mode mismatching between detected field and local oscillator. In this paper, we propose and analyze a new measurement method, which is realized by assisting the balanced homodyne detections with a high gain phase sensitive parametric amplifier. The employment of the high gain parametric amplifier helps to tackle the vacuum quantum noise originat…
I propose an iterative expectation maximization algorithm for reconstructing a quantum optical ensemble from a set of balanced homodyne measurements performed on an optical state. The algorithm applies directly to the acquired data, bypassing the intermediate step of calculating marginal distributions. The advantages of the new method are made manifest by comparing it with the traditional inverse Radon transformation technique.
A new method is described for determining the quantum correlations at different times in optical pulses by using balanced homodyne detection. The signal pulse and sequences of ultrashort test pulses are superimposed, where for chosen distances between the test pulses their relative phases and intensities are varied from measurement to measurement. The correlation statistics of the signal pulse is obtained from the time-integrated difference photocurrents measured.
A Simple and Robust Balanced Homodyne Detector for High-Repetition-Rate Pulsed Sources
Università degli Studi di Milano（米兰大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Milano（意大利国家核物理研究所，米兰分部）；Istituto di Fotonica e Nanotecnologie - CNR（光子学与纳米技术研究所-国家研究委员会）
We present a comprehensive theory and an easy to follow method for the design and construction of a wideband homodyne detector for time-domain quantum measurements. We show how one can evaluate the performance of a detector in a specific time-domain experiment based on electronic spectral characteristic of that detector. We then present and characterize a high-performance detector constructed using inexpensive, commercially available components such as low-noise high-speed operational amplifiers and high-bandwidth photodiodes. Our detector shows linear behavior up to a level of over 13 dB clea…
The technique of almost-balanced weak values amplification (ABWV) was recently proposed [Phys. Rev. Lett. 116: 100803 (2016)]. We demonstrate this technique using a modified Sagnac interferometer, where the counter-propagating beams are spatially separated. The separation between the two beams provides additional amplification, with respect to using colinear beams in a Sagnac interferometer. As a demonstration of the technique, we perform measurements of the angular velocity in one of the mirrors of the interferometer. Within the same setup, the weak-value amplification technique is also perfo…
Balanced homodyne detector (BHD) that can measure the field quadratures of coherent states has been widely used in a range of quantum information technologies. Generally, the BHD tends to suffer from narrow bands and an expanding bandwidth behavior usually traps into a compromise with the gain, electronic noise, and quantum to classical noise ratio, etc. In this paper, we design and construct a wideband BHD based on radio frequency and integrated circuit technology. Our BHD shows bandwidth behavior up to 1.2 GHz and its quantum to classical noise ratio is around 18 dB. Simultaneously, the BHD …
We design and demonstrate on-chip homodyne detection operating in the quantum regime, i.e. able to detect genuine nonclassical features. Our setup exploits a glass-integrated homodyne analyzer (IHA) entirely fabricated by femtosecond laser micromachining. The IHA incorporates on the same chip a balanced waveguide beam splitter and a thermo-optic phase shifter, allowing us to record homodyne traces at different phases and to perform reliable quantum state tomography. In particular, we show that the IHA allows for the detection of nonclassical features of continuous-variable quantum states, such…
We show that the full statistics of the two detectors outputs in a balanced homodyne detection setup involving a local oscillator in an ideal coherent state is experimentally accessible despite the excess noise existing in actual laser sources. This possibility is illustrated using phase randomized coherent states signals from which the statistics of Fock states can accurately be obtained. The experimental verification of the recently predicted [Kühn and Vogel, Phys. Rev. A, \textbf{98}, 013832 (2018)] two-detector correlation probability for Fock states is presented for states $\vert 1 \rangl…
Protocols for probabilistic entanglement-assisted quantum teleportation and for entanglement swapping of material qubits are presented. They are based on a protocol for postselective Bell-state projection which is capable of projecting two material qubits onto a Bell state with the help of ancillary coherent multiphoton states and postselection by balanced homodyne photodetection. Provided this photonic postselection is successful we explore the theoretical possibilities of realizing unit fidelity quantum teleportation and entanglement swapping with $25\%$ success probability. This photon-assi…
Photonic quantum technology can be enhanced by monolithic fabrication of both the underpinning quantum hardware and the corresponding electronics for classical readout and control. Together, this enables miniaturisation and mass-manufacture of small quantum devices---such as quantum communication nodes, quantum sensors and sources of randomness---and promises the precision and scale of fabrication required to assemble useful quantum computers. Here we combine CMOS compatible silicon and germanium-on-silicon nano-photonics with silicon-germanium integrated amplification electronics to improve p…
The advent of stable, highly squeezed states of light has generated great interest in the gravitational wave community as a means for improving the quantumnoise- limited performance of advanced interferometric detectors. To confidently measure these squeezed states, it is first necessary to measure the shot-noise across the frequency band of interest. Technical noise, such as non-stationary events, beam pointing, and parasitic interference, can corrupt shot-noise measurements at low Fourier frequencies, below tens of kilo-Hertz. In this paper we present a qualitative investigation into all of …
Using coherent phase states, parameterized phase state distributions for a single-mode radiation field are introduced and their integral relation to the phase-parameterized field-strength distributions is studied. The integral kernel is evaluated and the problem of direct sampling of the coherent phase state distributions using balanced homodyne detection is considered. Numerical simulations show that when the value of the smoothing parameter is not too small the coherent phase state distributions can be obtained with sufficiently well accuracy. With decreasing value of the smoothing parameter…
We provide a detailed analysis of the recently proposed setup for a loophole-free test of Bell inequality using conditionally generated non-Gaussian states of light and balanced homodyning. In the proposed scheme, a two-mode squeezed vacuum state is de-gaussified by subtracting a single photon from each mode with the use of an unbalanced beam splitter and a standard low-efficiency single-photon detector. We thoroughly discuss the dependence of the achievable Bell violation on the various relevant experimental parameters such as the detector efficiencies, the electronic noise and the mixedness …
Quantum states of light having a Wigner function with negative values represent a key resource in quantum communication and quantum information processing. Here, we present the generation of such a state at the telecommunication wavelength of 1550nm. The state is generated by means of photon subtraction from a weakly squeezed vacuum state and is heralded by the `click' of a single photon counter. Balanced homodyne detection is applied to reconstruct the Wigner function, also yielding the state's photon number distribution. The heralding photons are frequency up-converted to 532nm to allow for …
We demonstrate a die-level balanced homodyne receiver for coherent optical access and continuous-variable quantum applications, featuring a 40dB CMRR up to 1GHz and a high quantum-to-classical noise ratio of 26.8dB at 12.3mW of LO power. 500Mb/s QPSK transmission was accomplished with a sensitivity of -55.8dBm.
Variable measurement operators enable the optimization of strategies for testing quantum properties and the preparation of a range of quantum states. Here, we experimentally implement a weak-field homodyne detector that can continuously tune between measuring photon numbers and field quadratures. We combine a quantum signal with a coherent state on a balanced beam splitter and detect light at both output ports using photon-number-resolving transition edge sensors. We observe that the discrete difference statistics converge to the quadrature distribution of the signal as we increase the coheren…
Sagnac speed meter (SSM) topology is known as an alternative technique to reduce quantum back-action in gravitational-wave interferometers. However, any potential imbalance of the main beamsplitter was shown to reduce the quantum noise superiority of speed meter at low frequencies, caused due to increased laser noise coupling to the detection port. In this paper, we show that implementing balanced homodyne readout scheme and for a particular choice of the local oscillator (LO) delivery port, the excess laser noise contribution to quantum noise limited sensitivity (QNLS) is partly compensated a…
Optical homodyne detection has found use in a range of quantum technologies as both a characterisation tool and as a way to post-selectively generate non-linearities. So far optical implementations have been limited to bulk optics. Here we present the first homodyne detector fully integrated with silicon photonics and suitable for measurements of the quantum state of the electromagnetic field. This high speed, compact detector shows low noise operation, with 10 dB of clearance between shot noise and electronic noise, up to a speed of 160 MHz. These performances are suitable for on-chip charact…
The balanced homodyne detection as a readout scheme of gravitational-wave detectors is carefully examined from the quantum field theoretical point of view. The readout scheme in gravitational-wave detectors specifies the directly measured quantum operator in the detection. This specification is necessary when we apply the recently developed quantum measurement theory to gravitational-wave detections. We examine the two models of measurement. One is the model in which the directly measured quantum operator at the photodetector is Glauber's photon number operator, and the other is the model in w…
We review experimental work on the measurement of the quantum state of optical fields, and the relevant theoretical background. The basic technique of optical homodyne tomography is described with particular attention paid to the role played by balanced homodyne detection in this process. We discuss some of the original single-mode squeezed-state measurements as well as recent developments including: other field states, multimode measurements, array detection, and other new homodyne schemes. We also discuss applications of state measurement techniques to an area of scientific and technological…
With the recent discovery of Gravitational waves, marking the start of the new field of GW astronomy, the push for building more sensitive laser-interferometric gravitational wave detectors (GWD) has never been stronger. Balanced homodyne detection (BHD) allows for a quantum noise limited readout of arbitrary light field quadratures, and has therefore been suggested as a vital building block for upgrades to Advanced LIGO and third generation observatories. In terms of the practical implementation of BHD, we develop a full framework for analyzing the static optical high order modes (HOMs) occur…
Cavity-assisted homodyne detection with a single photodiode
Institute for Applied Physics, Friedrich Schiller University Jena（耶拿弗里德里希·席勒大学应用物理研究所）；Abbe Center of Photonics, Friedrich Schiller University Jena（耶拿弗里德里希·席勒大学阿贝光子学中心）
Using a recent result of Albini et al. to represent quantum homodyne tomography in terms of a single observable (as a normalized positive operator measure) we construct a generalized Markov kernel which transforms (the measurement outcome statistics of) this observable into (the measurement outcome statistics of) a covariant phase space observable. We also consider the inverse question. Finally, we add some remarks on the quantum theoretical justification of the experimental implementations of these observables in terms of balanced homodyne and 8-port detection techniques, respectively.
We propose a legitimate and easily computable nonclassicality indicator for the states of electromagnetic fields based on the standard deviation in the measurement of the homodyne rotated quadrature operator. The proposed nonclassicality indicator is the nonclassical area projected by the optical tomogram of the quantum state of light on the optical tomographic plane. If the nonclassical area projected by the optical tomogram of a quantum state is greater than zero, the state is nonclassical, and the area is zero for the pure classical state. It is also noted that the nonclassical area of a qu…
Heisenberg-scaling characterization of a two-channel optical network via two-port homodyne detection
School of Mathematics and Physics, University of Portsmouth（朴茨茅斯大学数学与物理学院）；Quantum Science and Technology Hub, University of Portsmouth（朴茨茅斯大学量子科学与技术中心）；Dipartimento di Fisica, Università di Bari & Politecnico di Bari（巴里大学与巴里理工大学物理系）；INFN, Sezione di Bari（意大利国家核物理研究所巴里分部）；Institute of Cosmology and Gravitation, University of Portsmouth（朴茨茅斯大学宇宙学与引力研究所）
We propose and experimentally verify a novel method for the remote preparation of entangled bits (ebits) made of a single-photon coherently delocalized in two well-separated temporal modes. The proposed scheme represents a remotely tunable source for tailoring arbitrary ebits, whether maximally or non-maximally entangled, which is highly desirable for applications in quantum information technology. The remotely prepared ebit is studied by performing homodyne tomography with an ultra-fast balanced homodyne detection scheme recently developed in our laboratory.
We propose a Procrustean entanglement concentration scheme for continuous variable states inspired by the scheme proposed in Fiurasek et. al. Phys. Rev. A 67, 022304, (2003). We show that the eight-port homodyne measurement of Fiurasek et. al. Phys. Rev. A 67, 022304, (2003) can be replaced by a balanced homodyne measurement with the advantage of providing a success criterion that allows Alice and Bob to determine if entanglement concentration was achieved. In addition, it facilitates a straightforward and feasible experimental implementation.
We discuss a balanced homodyne detection scheme with imperfect detectors in the framework of the operational approach to quantum measurement. We show that a realistic homodyne measurement is described by a family of operational observables that depends on the experimental setup, rather than a single field quadrature operator. We find an explicit form of this family, which fully characterizes the experimental device and is independent of a specific state of the measured system. We also derive operational homodyne observables for the setup with a random phase, which has been recently applied in …
We present the observation of optical fields carrying squeezed vacuum states at sideband frequencies from 10Hz to above 35MHz. The field was generated with type-I optical parametric oscillation below threshold at 1064nm. A coherent, unbalanced classical modulation field at 40MHz enabled the generation of error signals for stable phase control of the squeezed vacuum field with respect to a strong local oscillator. Broadband squeezing of approximately -4dB was measured with balanced homodyne detection. The spectrum of the squeezed field allows a quantum noise reduction of ground-based gravitatio…
We describe a novel tool for the quantum characterization of optical devices. The experimental setup involves a stable reference state that undergoes an unknown quantum transformation and is then revealed by balanced homodyne detection. Through tomographic analysis on the homodyne data we are able to characterize the signal and to estimate parameters of the interaction, such as the loss of an optical component, or the gain of an amplifier. We present experimental results for coherent signals, with application to the estimation of losses introduced by simple optical components, and show how the…
We implement a quantum random number generator based on a balanced homodyne measurement of vacuum fluctuations of the electromagnetic field. The digitized signal is directly processed with a fast randomness extraction scheme based on a linear feedback shift register. The random bit stream is continuously read in a computer at a rate of about 480 Mbit/s and passes an extended test suite for random numbers.
