Entangled Beams Research Articles

Two-photon absorption cross sections of pulsed entangled beams.

Entangled two-photon absorption (ETPA) could form the basis of nonlinear quantum spectroscopy at very low photon fluxes, since, at sufficiently low photon fluxes, ETPA scales linearly with the photon flux. When different pairs start to overlap temporally, accidental coincidences are thought to give rise to a "classical" quadratic scaling that dominates the signal at large photon fluxes and, thus, recovers a supposedly classical regime, where any quantum advantage is thought to be lost. Here, we scrutinize this assumption and demonstrate that quantum-enhanced absorption cross sections can persist even for very large photon numbers. To this end, we use a minimal model for quantum light, which can interpolate continuously between the entangled pair and a high-photon-flux limit, to analytically derive ETPA cross sections and the intensity crossover regime. We investigate the interplay between spectral and spatial degrees of freedom and how linewidth broadening of the sample impacts the experimentally achievable enhancement.

Underwater entanglement propagation of auto-focusing Airy beams.

In underwater wireless optical communication, orbital angular momentum (OAM) states suffer from turbulence distortions. This study aims to investigate the effectiveness of auto-focusing and OAM entanglement of the beams in reducing the turbulence effects. We implement the single-phase approximation and the extended Huygens-Fresnel principle to derive the detection probability of the entangled Airy beams under unstable oceanic turbulence. The results show that auto-focusing can protect the signal OAM mode and suppress modal crosstalks, while entangled OAM states can further enhance the resistance against oceanic turbulence around the focus position. The numerical analysis demonstrates that after the auto-focusing position, the beams evolve in completely opposite directions, indicating that the focal length should be modulated according to the length of a practical link to enhance received signals. These findings suggest that entangled auto-focusing vortex beams may be a desirable light source in underwater communication systems.

Quadripartite entanglement from two-port resonator with second-order harmonic generation

Quantum entanglement is a crucial resource for performing quantum computing and constructing quantum communication networks. The preparation and manipulation of entangled light field are the basic elements of quantum communication. With the development of science and technology, multicolor multipartite entanglement is becoming a kind of special resource for quantum information, quantum networks, and quantum memory. In this paper, we propose a scheme of generating quadripartite entanglement among four output beams from a two-port frequency doubling resonator, in which a type-II phase matching nonlinear crystal is placed. We make two fundamental-frequency pump beams with the same frequency and vertical polarization pass through the nonlinear crystal to produce two frequency-doubling beams. There is a quadripartite entanglement between the frequency-doubling beams, which are output at two ports of the optical resonator, and the incident fundamental beams. Based on the transmission matrix from the coupled wave equation, the self-consistent equations of the intracavity modes and the corresponding noise properties of the output modes can be obtained. Then, the quadripartite entanglement produced from two second harmonic beams and two reflected fundamental-frequency pump beams, is verified by using the positive partial transposition criterion, in a wide range of pumping power and analysis frequency. The setup proposed in this work is compact and experimentally feasible. It is also convenient to separate the four entangled beams spatially, with different wavelengths and polarizations. When the beam wavelengths are matched with 1560 nm (low loss window of fiber) and 780 nm (atomic absorption line of Rb), this scheme can be more useful in both quantum communication and quantum memory.

Nonlocal phase modulation of multimode, continuous-variable twin beams

We investigate experimentally the nonlocal phase modulation of multiple-frequency-mode, continuous-variable entangled twin beams. We use a pair of electro-optical phase modulators to modulate the entangled probe and conjugate light beams produced by four-wave mixing in hot rubidium vapor. A single phase modulator in either one of the twin beams reduces the two-mode squeezing signal. The overall quantum entanglement is preserved, however, as the modulator nonlocally distributes the beam correlations among frequency modes of the multimode fields. The two-mode squeezing can be recovered by reversing the mixing with an additional out-of-phase electro-optical phase modulator (EOM) in the other beam.

Phase sensitivity with a coherent beam and twin beams via intensity difference detection

We focus on the Mach–Zehnder interferometer (MZI) with the input of a coherent beam and one of the bright entangled twin beams with an external power reference beam employed for measurement. The results show that the phase sensitivity can reach sub-Heisenberg limit and approach quantum Cramér–Rao bound by changing the squeezing parameters and the photon number of the coherent beam, under the phase-matching condition. The absence of the external power reference beam will degrade the performance of the phase sensitivity. Meanwhile, this scheme shows good robustness against the losses of the photon detectors. We present a detailed discussion about the phase sensitivities when the inputs are two coherent beams, or a coherent beam plus a single-mode squeezed vacuum beam based on the MZI. This scenario can be applied in the field of phase precision measurements and other optical sensors.

Information encoding in the spatial correlations of entangled twin beams.

The ability to use the temporal and spatial degrees of freedom of quantum states of light to encode and transmit information is crucial for a robust and efficient quantum network. In particular, the potential offered by the large dimensionality of the spatial degree of freedom remains unfulfilled, as the necessary level of control required to encode information remains elusive. We encode information in the distribution of the spatial correlations of entangled twin beams by taking advantage of their dependence on the angular spectrum of the pump needed for four-wave mixing. We show that the encoded information can only be extracted through joint spatial measurements of the twin beams and not through individual beam measurements and that the temporal quantum correlations are not modified. The ability to engineer the spatial properties of twin beams will enable high-capacity quantum networks and quantum-enhanced spatially resolved sensing and imaging.

Quantum magnetic gradiometer with entangled twin light beams.

In the past few decades, optical magnetometry has experienced remarkable development and reached to an outstanding sensitivity. For magnetometry based on optical readout of atomic ensemble, the fundamental limitation of sensitivity is restricted by spin projection noise and photon shot noise. Meanwhile, in practical applications, ambient magnetic noise also greatly limits the sensitivity. To achieve the best sensitivity, it is essential to find an efficacious way to eliminate the noises from different sources, simultaneously. Here, we demonstrate a quantum magnetic gradiometer with sub-shot-noise sensitivity using entangled twin beams with differential detection. The quantum enhancement spans a frequency range from 7 Hz to 6 MHz with maximum squeezing of 5.5 dB below the quantum noise limit. The sensitivity of gradiometer reaches 18 fT/cm[Formula: see text] at 20 Hz. Our study inspires future possibilities to use quantum-enhanced technology in developing sensitive magnetometry for practical applications in noisy and physically demanding environments.

Computing Shor’s algorithmic steps with interference patterns of classical light

When considered as orthogonal bases in distinct vector spaces, the unit vectors of polarization directions and the Laguerre–Gaussian modes of polarization amplitude are inseparable, constituting a so-called classical entangled light beam. Equating this classical entanglement to quantum entanglement necessary for computing purpose, we show that the parallelism featured in Shor’s factoring algorithm is equivalent to the concurrent light-path propagation of an entangled beam or pulse train. A gedanken experiment is proposed for executing the key algorithmic steps of modular exponentiation and Fourier transform on a target integer N using only classical manipulations on the amplitudes and polarization directions. The multiplicative order associated with the sought-after integer factors is identified through a four-hole diffraction interference from sources obtained from the entangled beam profile. The unique mapping from the fringe patterns to the computed order is demonstrated through simulations for the case N=15.

Enhanced Electro-optic Sampling with Quantum Probes.

Employing electro-optic sampling (EOS) with ultrashort probe pulses, recent experiments showed direct measurements of quantum vacuum fields and their correlations on subcycle timescales. Here, we propose a quantum-enhanced EOS where bright photon-number entangled twin beams are used to derive conditioned nonclassical probes. In the case of the quantum vacuum, this leads to a sixfold improvement in the signal-to-noise ratio over the classically probed EOS. In addition, engineering of the conditioning protocol yields a reliable way to extract higher-order moments of the quantum noise distribution and robust discrimination of the input quantum states, for instance, a vacuum and a few-photon cat state. These improvements open a viable route toward robust tomography of quantum fields in space-time, an equivalent of homodyne detection in energy-momentum space, and the possibility of precise experiments in real-space quantum electrodynamics.

State transfer with separable optical beams and variational quantum algorithms with classical light

Classical electromagnetic fields and quantum mechanics obey the principle of superposition alike. This opens up many avenues for simulation of a large variety of phenomena and algorithms, which have hitherto been considered quantum mechanical. In this paper, we propose two such applications. In the first, we introduce a new, to the best of our knowledge, class of beams, called “equivalent optical beams,” in parallel with equivalent states introduced in Phys. Rev. A 89, 062110 (2014)PLRAAN1050-294710.1103/PhysRevA.89.062110. These beams have the same information content for all practical purposes. Employing them, we show how to transfer information from one degree of freedom of classical light to another, without need for classically entangled beams. Next, we show that quantum machine learning can be performed with OAM beams through the implementation of a quantum classifier circuit. We provide explicit protocols and explore the possibility of their experimental realization.

Low-Noise Intensity Amplification of a Bright Entangled BeamSupported by the Innovation Program of Shanghai Municipal Education Commission (Grant No. 2021-01-07-00-08-E00100), the National Natural Science Foundation of China (Grant Nos. 11874155, 91436211, and 11374104), the Basic Research Project of Shanghai Science and Technology Commission (20JC1416100), the Natural Science Foundation of Shanghai (Grant No. 17ZR1442900); Minhang Leading Talents (Grant No. 201971), the

We experimentally demonstrate a low-noise phase-sensitive amplifier (PSA) scheme that is able to amplify bright entangled beams at a high level intensity gain of up to 4.4. Moreover, we demonstrate that the PSA scheme introduces much less uncorrelated extra noise to the entangled state than the phase-insensitive amplifier scheme with the same intensity gain. This PSA scheme has potential applications for quantum communication in continuous variable regimes.

Generating Two Continuous Entangled Microwave Beams Using a dc-Biased Josephson Junction

We show experimentally that a dc-biased Josephson junction in series with two microwave resonators emits entangled beams of microwaves leaking out of the resonators. In the absence of a stationary phase reference for characterizing the entanglement of the outgoing beams, we measure second-order coherence functions for proving entanglement up to an emission rate of 2.5 billion photon pairs per second. The experimental results are found in quantitative agreement with theory, proving that the low frequency noise of the dc bias is the main limitation for the coherence time of the entangled beams. This agreement allows us to evaluate the entropy of entanglement of the resonators, and to identify the improvements that could bring this device closer to a useful bright source of entangled microwaves for quantum-technological applications.

Deterministic generation of genuine tri-partite hybrid atom–photon entanglement through dissipation

The ability to deterministically generate genuine multi-partite entanglement is fundamental for the advancement of quantum information science. We show that the interaction between entangled twin beams of light and an atomic ensemble under conditions for electromagnetically induced transparency leads to the generation of genuine hybrid tri-partite entanglement between the two input fields and the atomic ensemble. In such a configuration, the system is driven through dissipation to a steady state given by the hybrid entangled state. To show the presence of the genuine hybrid entanglement, we introduce a new approach to treat the atomic operators that makes it possible to show a violation of a tri-partite entanglement criterion based on the properties of the two optical fields and collective properties of the atomic ensemble. Additionally, we show that while neither of the input optical fields exhibits single beam quadrature squeezing, as the fields propagate through the atomic medium, their individual quadratures can become squeezed and in some cases oscillate between the presence and absence of squeezing. Finally, we propose a technique to characterize the tri-partite entanglement through joint measurements of the fields leaving the atomic medium, making such an approach experimentally accessible.

Ultra-sensitive phase measurement based on an SU(1,1) interferometer employing external resources and substract intensity detection.

A new scheme has been proposed to realize the enhancement of phase sensitivity based on an SU(1,1) interferometer. Compared with the classical Mach-Zehnder interferometer, the SU(1,1) interferometer is splitted and recombined by an optical parametric amplifier and the phase sensitivity can beat shot noise limit by adjusting the parametric strength. In this model, the inputs of the SU(1,1) interferometer are bright entangled twin beams generated from four wave mixing and the detection method is substract intensity difference with one of the twin beams entering into the interferometer. The detection efficiency of the detector is taken into consideration. This scheme also proves that when one of the inputs of an SU(1,1) interferometer is an vacuum beam, the phase sensitivity can beat shot noise limit by employing substract intensity detection and external resources.

Probing excited-state dynamics with quantum entangled photons: Correspondence to coherent multidimensional spectroscopy.

Quantum light is a key resource for promoting quantum technology. One such class of technology aims to improve the precision of optical measurements using engineered quantum states of light. In this study, we investigate transmission measurement of frequency-entangled broadband photon pairs generated via parametric down-conversion with a monochromatic laser. It is observed that state-to-state dynamics in the system under study are temporally resolved by adjusting the path difference between the entangled twin beams when the entanglement time is sufficiently short. The non-classical photon correlation enables time-resolved spectroscopy with monochromatic pumping. It is further demonstrated that the signal corresponds to the spectral information along anti-diagonal lines of, for example, two-dimensional Fourier-transformed photon-echo spectra. This correspondence inspires us to anticipate that more elaborately engineered photon states would broaden the availability of quantum light spectroscopy.

Reconfigurable Hexapartite Entanglement by Spatially Multiplexed Four-Wave Mixing Processes.

Multipartite entanglement serves as a vital resource for quantum information processing. Generally, its generation requires complex beam splitting processes which limit scalability. A promising trend is to integrate multiple nonlinear processes into a single device via frequency or time multiplexing. The generated states in these schemes are useful for quantum computation. However, they are confined in one or two beams and hard to be spatially separated for applications in quantum communication. Here, we experimentally demonstrate a scheme to generate spatially separated hexapartite entangled states by means of spatially multiplexing seven concurrent four-wave mixing processes. In addition, we show that the entanglement structure characterized by subsystem entanglement distribution can be modified by appropriately shaping the pump characteristics. Such reconfigurability of the entanglement structure gives the possibility to target a desired multipartite entangled state for a specific quantum communication protocol. Our results here provide a new platform for generating large scale spatially separated reconfigurable multipartite entangled beams.

Unveiling contextual realities by microscopically entangling a neutron

The development of qualitatively new measurement capabilities is often a prerequisite for critical scientific and technological advances. Here we introduce an unconventional quantum probe, an entangled neutron beam, where individual neutrons can be entangled in spin, trajectory and energy. The spatial separation of trajectories from nanometers to microns and energy differences from peV to neV will enable investigations of microscopic magnetic correlations in systems with strongly entangled phases, such as those believed to emerge in unconventional superconductors. We develop an interferometer to prove entanglement of these distinguishable properties of the neutron beam by observing clear violations of both Clauser-Horne-Shimony-Holt and Mermin contextuality inequalities in the same experimental setup. Our work opens a pathway to a future of entangled neutron scattering in matter.

Optimal phase sensitivity by quantum squeezing based on a Mach–Zehnder interferometer

A novel scheme for the enhancement of phase sensitivity based on a Mach–Zehnder interferometer (MZI) and intensity detection is proposed. With the input of bright entangled twin beams from four wave mixing (FWM), the phase sensitivity can beat shot noise limit (SNL) and approach Heisenberg limit. This scheme is special due to that only one of bright entangled twin beams enters into the MZI and the other one is employed for measurement. In addition, by altering the parametric strength of FWM and the implementation of maximum quantum squeezing, the optimal phase sensitivity can reach sub-SNL. Optical intensity depletion of photon detectors and internal intensity depletion of the MZI are also discussed. The scheme displays that by employing external resources, while one input of the MZI is an vacuum beam, the phase sensitivity still can beat SNL.

Optomechanically induced entanglement

We present a special quantum phenomenon named optomechanically induced entanglement in the conventional single-cavity optomechanical system driven by a strong pump input field and a relatively weak probe input field. Bipartite entanglement between the pump and probe output fields can be achieved under realistic experimental conditions when the input pump (probe) field is blue detuned by the mechanical frequency (resonant) with respect to the cavity field. The physical origin is the mechanical oscillator displacement, which plays a role similar to the atomic coherence for the well-known electromagnetically induced transparency in the traditional \ensuremath{\Lambda}-type atomic system. This scheme provides an alternative, convenient way to generate nondegenerate entangled bright light beams by using only coherent laser fields, and may bring great facility in realistic quantum information processing protocols.

Scheme for enhancing quadripartite entangled optical modes from an opto-mechanical system

Multipartite entanglement is a key resource for quantum information processing and quantum communication. We show that the robust entanglement among four filtered output optical modes can be achieved when there is a nonlinear crystal inside an optomechanical cavity. The optical parametric amplifier (OPA) gives rise to single-mode squeezing of the cavity modes; therefore, the entanglement among four output optical modes can be enhanced remarkably. Furthermore, the degree of quadripartite entanglement is influenced by the nonlinear gain of OPA and bandwidth of the filters. Large entanglement can be obtained by optimizing the filter functions, which is important for utilizing entangled light beams more efficiently in real experiments. This kind of multipartite entanglement will be useful and valuable in the area of quantum communication networks.