Joint measurement of multiple noncommuting parameters

Although quantum metrology allows us to make precision measurements beyond the standard quantum limit, it mostly works on the measurement of only one observable due to the Heisenberg uncertainty relation on the measurement precision of noncommuting observables for one system. In this paper, we study the schemes of joint measurement of multiple observables which do not commute with each other using the quantum entanglement between two systems. We focus on analyzing the performance of a SU(1,1) nonlinear interferometer on fulfilling the task of joint measurement. The results show that the information encoded in multiple noncommuting observables on an optical field can be simultaneously measured with a signal-to-noise ratio higher than the standard quantum limit, and the ultimate limit of each observable is still the Heisenberg limit. Moreover, we find a resource conservation rule for the joint measurement

Quantum information tapping using a fiber optical parametric amplifier with noise figure improved by correlated inputs

One of the important function in optical communication system is the distribution of information encoded in an optical beam. It is not a problem to accomplish this in a classical system since classical information can be copied at will. However, challenges arise in quantum system because extra quantum noise is often added when the information content of a quantum state is distributed to various users. Here, we experimentally demonstrate a quantum information tap by using a fiber optical parametric amplifier (FOPA) with correlated inputs, whose noise is reduced by the destructive quantum interference through quantum entanglement between the signal and the idler input fields. By measuring the noise figure of the FOPA and comparing with a regular FOPA, we observe an improvement of 0.7+-0.1 dB and 0.84+-0.09 dB from the signal and idler outputs, respectively. When the low noise FOPA functions as an information splitter, the device has a total information transfer coefficient of Ts+Ti=1.47+-0.2, which is greater than the classical limit of 1. Moreover, this fiber based device works at the 1550 nm telecom band, so it is compatible with the current fiber-optical network.Comment: 28 pages, 6 figure

Quantum enhanced joint measurement of two conjugate observables with an SU(1, 1) interferometer

We jointly measure the phase and amplitude modulation of an optical field with the newly developed SU(1,1) interferometer. We simultaneously achieve a signal-to-noise ratio improvement of 1.1 and 1 dB over the standard quantum limit in amplitude and phase measurement

Approaching single temporal mode operation in twin beams generated by pulse pumped high gain spontaneous four wave mixing

By investigating the intensity correlation function, we study the spectral/temporal mode properties of twin beams generated by the pulse-pumped high gain spontaneous four wave mixing (SFWM) in optical fiber from both the theoretical and experimental aspects. The results show that the temporal property depends not only on the phase matching condition and the filters applied in the signal and idler fields, but also on the gain of SFWM. When the gain of SFWM is low, the spectral/temporal mode properties of the twin beams are determined by the phase matching condition and optical filtering and are usually of multi-mode nature, which leads to a value larger than 1 but distinctly smaller than 2 for the normalized intensity correlation function of individual signal/idler beam. However, when the gain of SFWM is very high, we demonstrate the normalized intensity correlation function of individual signal/idler beam approaches to 2, which is a signature of single temporal mode. This is so even if the frequencies of signal and idler fields are highly correlated so that the twin beams have multiple modes in low gain regime. We find that the reason for this behavior is the dominance of the fundamental mode over other higher order modes at high gain. Our investigation is useful for constructing high quality multi-mode squeezed and entangled states by using pulse-pumped spontaneous parametric down-conversion and SFWM

Versatile and precise quantum state engineering by using nonlinear interferometers

The availability of photon states with well-defined temporal modes is crucial for photonic quantum technologies. Ever since the inception of generating photonic quantum states through pulse pumped spontaneous parametric processes, many exquisite efforts have been put on improving the modal purity of the photon states to achieve single-mode operation. However, because the nonlinear interaction and linear dispersion are often mixed in parametric processes, limited successes have been achieved so far only at some specific wavelengths with sophisticated design. In this paper, we resort to a different approach by exploiting an active filtering mechanism originated from interference fringe of nonlinear interferometer. The nonlinear interferometer is realized in a sequential array of nonlinear medium, with a gap in between made of a linear dispersive medium, in which the precise modal control is realized without influencing the phase matching of the parametric process. As a proof-of-principle demonstration of the capability, we present a photon pairs source using a two-stage nonlinear interferometer formed by two identical nonlinear fibers with a standard single mode fiber in between. The results show that spectrally correlated two-photon state via four wave mixing in a single piece nonlinear fiber is modified into factorable state and heralded single-photons with high modal purity and high heralding efficiency are achievable. This novel quantum interferometric method, which can improve the quality of the photon states in almost all the aspects such as modal purity, heralding efficiency, and flexibility in wavelength selection, is proved to be effective and easy to realize

Loss-tolerant quantum dense metrology with SU(1,1) interferometer

Heisenberg uncertainty relation in quantum mechanics sets the limit on the measurement precision of non-commuting observables in one system, which prevents us from measuring them accurately at the same time. However, quantum entanglement between two systems allows us to infer through Einstein-Podolsky-Rosen correlations two conjugate observables with precision better than what is allowed by Heisenberg uncertainty relation. With the help of the newly developed SU(1,) interferometer, we implement a scheme to jointly measure information encoded in multiple non-commuting observables of an optical field with a signal-to-noise ratio improvement of about 20% over the classical limit on all measured quantities simultaneously. This scheme can be generalized to the joint measurement of information in arbitrary number of non-commuting observables

Quantum state engineering by nonlinear quantum interference

Multiphoton quantum interference is the underlying principle for optical quantum information processing protocols. Indistinguishability is the key to quantum interference. Therefore, the success of many protocols in optical quantum information processing relies on the availability of photon states with a well-defined spatial and temporal mode. Photons in single spatial mode can be obtained from nonlinear processes in single-mode waveguides. For the temporal mode, the common approach is to engineer the nonlinear processes so as to achieve the required spectral properties for the generated photons. But, this approach is complicated because the spectral properties and the nonlinear interaction are often intertwined through phase-matching condition. In this paper, we study a different approach that separates the spectral control from nonlinear interaction, leading to versatile and precise engineering of the spectral properties of nonlinear parametric processes. The approach is based on an SU(1,1) nonlinear interferometer with a pulsed pump and a controllable linear spectral phase shift for precise engineering. We systematically analyze the important figures of merit such as modal purity and heralding efficiency in characterizing a photon state and use this analysis to investigate the feasibility of this interferometric approach. Specifically, we analyze in detail the requirement on the spectral phase engineering to optimize the figures of merit and apply numerical simulations to the nonlinear four-wave mixing process in dispersion-shifted fibers with a standard single-mode fiber as the phase control medium. Both modal purity and efficiency are improved simultaneously with this technique. Furthermore, a multistage nonlinear interferometer is proposed and shown to achieve more precise state engineering for near-ideal single-mode operation and near-unity efficiency. We also extend the study to the case of high pump power when the high gain is achieved in the four-wave mixing process for the spectral engineering of quantum entanglement in continuous variables. Our investigation provides an approach for precisely tailoring the spectral property of quantum light sources, especially, photon pairs can be engineered to simultaneously possess the features of high purity, high collection efficiency, high brightness, and high flexibility in wavelength and bandwidth selection

Granite is an Effective Helium Source Rock:Insights from the Helium Generation and Release Characteristics in Granites from the North Qinling Orogen, China

Global helium (He) shortage is a challenging problem; however, the types of helium source rock and the mechanisms of He generation and release therein remain still poorly understood. In this study, in order to evaluate the potential of granite as an effective helium source rock, we collected granitic samples from the North Qinling Orogen, Central China, in the south of the helium-rich Weihe Basin. The helium generation and release behaviors in granite were studied through analysis of U and Th concentrations, EMPA images, and He and Ar concentrations and isotopic ratios extracted by crushing and stepwise heating. The results indicate that Ar has a better retention and a lower mobility than He. 3He/4He ratios released by crushing and stepwise heating are 0.016–0.056 RA and 0.003–0.572 RA, respectively, where RA is the atmospheric 3He/4He of 1.4×10-6, reflecting a crustal and radiogenic source. Helium concentrations extracted by the two ways are 0.13–0.95 ucm3 STP/g and 7.82–115.62 ucm3 STP/g, respectively, suggesting that matrix-sited He accounts for more than 98% of total helium preserved in granite. In addition, the total generated He amounts in granites are calculated based on the measured U and Th concentrations in granitic samples. Dividing the preserved He quantities by the generated He amounts, it turned out that less than 10% of He produced since the formation of the granite is preserved in the rock over geological time, suggesting that more than 90% generated He can be transferred to the Weihe Basin. Temperature and fracture are the two critical factors controlling He release. Based on the relationship between He diffusivity of granites and temperature and the He closure temperatures of a variety of U- and Th-rich minerals (27–250°C), we estimate that He can be partially released out of granite at the depths 7800 m. Fractures provide effective transfer of free He from deep source rocks to shallow reservoirs. Finally, a model on granite as an effective helium source rock is established. We suggest exploring He resources in hydrocarbon basins with granitic basement (or adjacent to granite bodies), high geothermal field, and young active fractures

Pulsed entanglement measured by parametric amplifier assisted homodyne detection

Balanced homodyne detection relies on a beam splitter to superpose the weak signal input and strong local oscillator. However, recent investigation shows that a high gain phase sensitive amplifier (PSA) can be viewed as homodyne detector, in which the strong pump of PSA serves as the local oscillator [1]. Here, we analyze a new method of measuring the continuous variable entanglement by assisting a balanced homodyne detector with the PSA and implement it experimentally. Before measuring quadrature amplitude with the balanced homodyne detectors, two entangled fields generated from a pulse pumped fiber optical parametric amplifier are simultaneously coupled into the PSA. We find that the normalized noise for both the difference and sum of the quadrature amplitudes of the two entangled fields fall below the shot noise limit by about 4.6 dB, which is the record degree of entanglement measured in optical fiber systems. The experimental results illustrate that the advantages of the new measurement method include but not limit to tolerance to detection loss and characterizing entanglement with only one homodyne detector. The influence of mode-mismatching due to multi-mode property of entanglement on the measured noise reduction can also be greatly mitigated, indicating the new method is advantageous over the traditional measurement in multi-mode case

Measuring continuous-variable quantum entanglement with parametric-amplifier-assisted homodyne detection

The traditional method for measuring Einstein-Podolsky-Rosen-type continuous-variable quantum entanglement relies on balanced homodyne detections, which are sensitive to vacuum quantum noise coupled in through losses due to various factors such as detector quantum efficiency and mode mismatching between the detected field and the local oscillator. In this paper, we propose and analyze a measurement method, which is realized by assisting the balanced homodyne detections with a high-gain phase-sensitive parametric amplifier. The employment of the phase-sensitive amplifier helps us to tackle the vacuum quantum noise originating from detection losses. Moreover, because the high-gain phase-sensitive amplifier can couple two fields of different types, the proposed scheme can be used to reveal quantum entanglement between two fields of different types by using only one balanced homodyne detection. Furthermore, detailed analysis shows that in the multimode case, the proposed scheme is also advantageous over the traditional method. Such a measurement method should find wide applications in quantum information and quantum metrology involving measurement of continuous variables