Temporal coherence in an unbalanced SU(1,1) interferometer.

In classical coherence theory, coherence time is typically related to the bandwidth of the optical field. Narrowing the bandwidth by optical filtering will result in the lengthening of the coherence time. In the case of a delayed pulse photon interference, this will lead to pulse overlap and recovery of interference, which is otherwise absent due to time delay. However, this is changed for entangled optical fields. In this Letter, we investigate how the temporal coherence of the fields in a pulse-pumped SU(1,1) interferometer changes with the bandwidth of optical filtering. We find that the effect of optical filtering is not similar to the classical coherence theory in the presence of quantum entanglement. A full quantum theory is presented and can explain the phenomena well.

Propagation of temporal mode multiplexed optical fields in fibers: influence of dispersion.

Exploiting two interfering fields which are initially in the same temporal mode but with the spectra altered by propagating through different fibers, we characterize how the spectral profiles of temporal modes change with the fiber induced dispersion by measuring the fourth-order interference when the order number and bandwidth of temporal modes are varied. The experiment is done by launching a pulsed field in different temporal modes into an unbalanced Mach-Zehnder interferometer, in which the fiber lengths in two arms are different. The results show that the mode mismatch of two interfering fields, reflected by the visibility and pattern of interference, is not only dependent upon the amount of unbalanced dispersion but also related to the order number of temporal mode. In particular, the two interfering fields may become orthogonal under a modest amount of unbalanced dispersion when the mode number of the fields is k ≥ 2. Moreover, we discuss how to recover the spectrally distorted temporal mode by measuring and compensating the transmission induced dispersion. Our investigation paves the way for further investigating the distribution of temporally multiplexed quantum states in fiber network.

SU(2)-in-SU(1,1) Nested Interferometer for High Sensitivity, Loss-Tolerant Quantum Metrology.

We present experimental and theoretical results on a new interferometer topology that nests a SU(2) interferometer, e.g., a Mach-Zehnder or Michelson interferometer, inside a SU(1,1) interferometer, i.e., a Mach-Zehnder interferometer with parametric amplifiers in place of beam splitters. This SU(2)-in-SU(1,1) nested interferometer (SISNI) simultaneously achieves a high signal-to-noise ratio (SNR), sensitivity beyond the standard quantum limit (SQL) and tolerance to photon losses external to the interferometer, e.g., in detectors. We implement a SISNI using parametric amplification by four-wave mixing (FWM) in Rb vapor and a laser-fed Mach-Zehnder SU(2) interferometer. We observe path-length sensitivity with SNR 2.2 dB beyond the SQL at power levels (and thus SNR) 2 orders of magnitude beyond those of previous loss-tolerant interferometers. We find experimentally the optimal FWM gains and find agreement with a minimal quantum noise model for the FWM process. The results suggest ways to boost the in-practice sensitivity of high-power interferometers, e.g., gravitational wave interferometers, and may enable high-sensitivity, quantum-enhanced interferometry at wavelengths for which efficient detectors are not available.

[XBP1 modulates hypoxia/reoxygenation injury in mouse renal tubular epithelial cells through TXNIP-NLRP3 signaling pathway].

Objective: To investigate the role and regulation mechanism of X box binding protein 1 (XBP1) for hypoxia/reoxygenation(H/R) injury in mouse renal tubular epithelial cells (TCMK-1) through thioredoxin interacting protein (TXNIP)-nucleotide-binding domain (NOD)-like receptor protein (TXNIP-NLRP3) signaling pathway. Methods: The cells were divided into 4 groups: si-NC group transfected with negative control siRNA (si-NC), si-XBP1 group transfected with siRNA targeting XBP1 (si-XBP1), si-NC+H/R group transfected with si-NC and exposed to H/R, and si-XBP1+H/R group transfected with si-XBP1 and exposed to H/R. The Annexin Ⅴ/PI double-staining method was used to detect cell apoptosis; The mitochondrial membrane potential (MMP) was determined by using JC-1 dye; The mitochondrial reactive oxygen species (mROS) was assessed by using MitoSOX™ dye. The interference efficiency of XBP1 was tested by Western blotting and quantitative real-time polymerase chain reaction. The expression levels of TXNIP, NLRP3 and IL-1ß protein were detected by Western blotting. The colocalization of mitochondria and TXNIP was detected by double-labeling immunofluorescent staining. The intergroup difference was compared by using an independent samples t-test. Results: Compared with the si-NC group, more mROS, apoptosis and lower MMP were observed in si-NC+H/R group. Compared with the si-NC+H/R group, less apoptosis (12.08±0.51 vs 19.01±1.80, P<0.05), mROS (34.63±0.64 vs 48.17±1.84, P<0.01) and higher MMP (1.03±0.11 vs 0.45±0.08, P<0.05) were observed in si-XBP1+H/R group. Down-regulation of XBP1U (protein: 1.31±0.18 vs 0.23±0.02, P<0.01; mRNA: 1.12±0.07 vs 0.38±0.01, P<0.001) and XBP1S (protein: 1.13±0.17 vs 0.28±0.07, P<0.01; mRNA: 8.39±0.63 vs 2.45±0.22, P<0.001) inhibited expression of TXNIP (0.15±0.02 vs 0.04±0.01, P<0.01), NLRP3 (1.13±0.12 vs 0.51±0.12, P<0.05) and IL-1ß (1.02±0.04 vs 0.19±0.06, P<0.001) during H/R. Meanwhile, TXNIP exhibited significantly much less colocalization with mitochondria in the si-XBP1+H/R group. Conclusion: Supression of XBP1 expression can effectively alleviate H/R-induced TCMK-1 cells injury, whose mechanism may be inhibition of TXNIP-induced NLRP3 inflammasome activation.

Direct Temporal Mode Measurement for the Characterization of Temporally Multiplexed High Dimensional Quantum Entanglement in Continuous Variables.

Field-orthogonal temporal mode analysis of optical fields has recently been developed for a new framework of quantum information science. However, so far, the exact profiles of the temporal modes are not known, which makes it difficult to achieve mode selection and demultiplexing. Here, we report a novel method that measures directly the exact form of the temporal modes. This, in turn, enables us to make mode-orthogonal homodyne detection with mode-matched local oscillators. We apply the method to a pulse-pumped, specially engineered fiber parametric amplifier and demonstrate temporally multiplexed multidimensional quantum entanglement of continuous variables in telecom wavelength. The temporal mode characterization technique can be generalized to other pulse-excited systems to find their eigenmodes for multiplexing in the temporal domain.

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.

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.

Non-Hermitian Magnon-Photon Interference in an Atomic Ensemble.

The interference of photons in a lossy beam splitter (BS) exhibits anticoalescence, which is surprising for bosons. Such a non-Hermitian system involving open quantum dynamics is of particular interest for quantum information processing and metrology. The Hermiticity of photonic devices is generally fixed according to the material, but is controllable at the interface of photons and atomic systems. Here, we demonstrate a tunable non-Hermitian BS for the interference between traveling photonic and localized magnonic modes. The crossover from a Hermitian to a non-Hermitian magnon-photon BS is achieved by controlling the coherent and incoherent interaction mediated by the excited levels of atoms, which is reconfigurable via the detuning of a control laser. A correlated interference pattern between the photons and magnons is demonstrated by such a non-Hermitian BS. Our system has the potential to operate with photons and magnons at the single-quanta level, and it provides a versatile quantum interface for studying the non-Hermitian quantum physics and parity-time symmetry.

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.

Absolute sensitivity of phase measurement in an SU(1,1) type interferometer.

Absolute sensitivity is measured for the phase measurement in an SU(1,1) type interferometer, and the results are compared to that of a Mach-Zehnder interferometer operated under the condition of the same intra-interferometer intensity. The interferometer is phase locked to a point with the largest quantum noise cancellation, and a simulated phase modulation is added in one arm of the SU(1,1) interferometer. Both the signal and noise level are estimated at the same frequency range, and we obtained 3 dB improvement in sensitivity for the SU(1,1) interferometer over the Mach-Zehnder interferometer. Our results demonstrate a direct phase estimation and may pave the way for practical applications of a nonlinear interferometer.

Quantum non-demolition measurement of photon number with atom-light interferometers.

When atoms are illuminated by an off-resonant field, the AC Stark effect will lead to phase shifts in atomic states. The phase shifts are proportional to the photon number of the off-resonant illuminating field. By measuring the atomic phase with newly developed atom-light hybrid interferometers, we can achieve quantum non-demolition measurement of the photon number of the optical field. In this paper, we analyze theoretically the performance of this QND measurement scheme by using the QND measurement criteria established by Holland et al [Phys. Rev. A 42, 2995 (1990)]. We find the quality of the QND measurement depends on the phase resolution of the atom-light hybrid interferometers. We apply this QND measurement scheme to a twin-photon state from parametric amplifier to verify the photon correlation in the twin beams. Furthermore, a sequential QND measurement procedure is analyzed for verifying the projection property of quantum measurement and for the quantum information tapping. Finally, we discuss the possibility for single-photon-number-resolving detection via QND measurement.

Distribution of entangled photon pairs over few-mode fibers.

Few-mode fibers (FMFs) have been recently employed in classical optical communication to increase the data transmission capacity. Here we explore the capability of employing FMF for long distance quantum communication. We experimentally distribute photon pairs in the forms of time-bin and polarization entanglement over a 1-km-long FMF. We find the time-bin entangled photon pairs maintain their high degree of entanglement, no matter what type of spatial modes they are distributed in. For the polarization entangled photon pairs, however, the degree of entanglement is maintained when photon pairs are distributed in LP 01 mode but significantly declines when photon pairs are distributed in LP 11 mode due to a mode coupling effect in LP 11 mode group. We propose and test a remedy to recover the high degree of entanglement. Our study shows, when FMFs are employed as quantum channels, selection of spatial channels and degrees of freedom of entanglement should be carefully considered.

Generation of frequency degenerate twin beams in Rb85 vapor.

We demonstrate a new phase-matching geometry for four-wave mixing processes in hot Rb85 vapor, in which all four fields propagate in different directions but two of them are degenerate in frequency. When used as a parametric amplifier with an injected seed, two types of quantum mechanically correlated twin-beam states, either frequency degenerate or nondegenerate, can be generated. The quantum noise reduction in the intensity difference is almost 7 dB for the nondegenerate type and nearly 5 dB for the degenerate type. The spatial nondegeneracy of the four waves allows a variety of configurations of parametric processes, leading to flexible control for both phase insensitive and sensitive parametric amplification. The spatially nondegenerate but frequency degenerate four-wave mixing process will find wide applications in quantum metrology, quantum communication, and quantum information of continuous variables.

88% conversion efficiency with an atomic spin wave mediated mode selection.

In studying quantum correlation and quantum memory of continuous variables of light fields and atoms, a crucial step is the retrieval of the quantum fields by converting an atomic spin wave to light, and retrieval efficiency is a crucial parameter. In this Letter, we implement a double-pass Raman scheme in Rb87 by incorporating coherent feedback. We find that the transfer efficiency from an atomic spin wave, which is generated from a Raman process in a high gain regime, to light fields is enhanced by the double-pass scheme as compared to the commonly used single-pass scheme. An atomic spin wave as high as 88% is read out, limited only by decoherence of the atomic spin waves. Our analysis shows that the enhancement effect is because a double-pass scheme introduced the coherent feedback mechanism which selects the spatial mode of an atomic spin wave via the correlated optical field and enhances the coupling efficiency between the atom and light. The correlations between the write-in and readout signals generated in such a two-pass Raman process are also better than the single-pass case. We believe such a two-pass scheme with feedback mechanism should be useful for studying continuous variables in quantum systems.

Effects of losses in the atom-light hybrid SU(1,1) interferometer.

Collective atomic excitation can be realized by the Raman scattering. Such a photon-atom interface can form an SU(1,1)-typed atom-light hybrid interferometer, where the atomic Raman amplification processes take the place of the beam splitting elements in a traditional Mach-Zehnder interferometer. We numerically calculate the phase sensitivities and the signal-to-noise ratios (SNRs) of this interferometer with the method of homodyne detection and intensity detection, and give their differences of the optimal phase points to realize the best phase sensitivities and the maximal SNRs from these two detection methods. The difference of the effects of loss of light field and atomic decoherence on measure precision is analyzed.

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

One of the important functions in a communication network is the distribution of information. 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 = 1.5 ± 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 for quantum information distribution.

Temporal Purity and Quantum Interference of Single Photons from Two Independent Cold Atomic Ensembles.

The temporal purity of single photons is crucial to the indistinguishability of independent photon sources for the fundamental study of the quantum nature of light and the development of photonic technologies. Currently, the technique for single photons heralded from time-frequency entangled biphotons created in nonlinear crystals does not guarantee the temporal-quantum purity, except using spectral filtering. Nevertheless, an entirely different situation is anticipated for narrow-band biphotons with a coherence time far longer than the time resolution of a single-photon detector. Here we demonstrate temporally pure single photons with a coherence time of 100 ns, directly heralded from the time-frequency entangled biphotons generated by spontaneous four-wave mixing in cold atomic ensembles, without any supplemented filters or cavities. A near-perfect purity and indistinguishability are both verified through Hong-Ou-Mandel quantum interference using single photons from two independent cold atomic ensembles. The time-frequency entanglement provides a route to manipulate the pure temporal state of the single-photon source.

Generation of continuous variable quantum entanglement using a fiber optical parametric amplifier.

We demonstrate the experimental generation of quadrature amplitude entanglement in the 1550 nm band by using a fiber optical parametric amplifier. The measured noise variances of the difference and sum of the quadrature amplitudes of the pulsed signal and idler twin beams fall below the shot noise limit by about 1 and 0.8 dB (4.2 and 3.6 dB after the correction for efficiency), respectively, showing that the inseparability criterion of Einstein-Podolsky-Rosen entanglement I<2 is satisfied. Our investigation reveals that the quality of the measured entanglement can be further improved by increasing the transmission efficiency of the twin beams and by optimizing the temporal mode matching of the two sets of homodyne detection systems.

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.

Complete temporal mode analysis in pulse-pumped fiber-optical parametric amplifier for continuous variable entanglement generation.

Mode matching plays an important role in measuring the continuous variable entanglement. For the signal and idler twin beams generated by a pulse pumped fiber optical parametric amplifier (FOPA), the spatial mode matching is automatically achieved in single mode fiber, but the temporal mode property is complicated because it is highly sensitive to the dispersion and the gain of the FOPA. We study the temporal mode structure and derive the input-output relation for each temporal mode of signal and idler beams after decomposing the joint spectral function of twin beams with the singular-value decomposition method. We analyze the measurement of the quadrature-amplitude entanglement, and find mode matching between the multi-mode twin beams and the local oscillators of homodyne detection systems is crucial to achieve a high degree of entanglement. The results show that the noise contributed by the temporal modes nonorthogonal to local oscillator may be much larger than the vacuum noise, so the mode mis-match can not be accounted for by merely introducing an effective loss. Our study will be useful for developing a source of high quality continuous variable entanglement by using the FOPA.