NOON States Research Articles

Generation of multiparticle entangled states of nitrogen-vacancy centers with carbon nanotubes

We propose an efficient scheme for generating multiparticle entangled states between two arrays of nitrogen-vacancy centers that interact with two magnetically coupled carbon nanotubes, respectively. We show that through adjusting the external driving microwave fields and the dc currents flowing through the nanotube mechanical resonators, the multiparticle entanglement between the separated arrays of NV centers can be engineered and tuned dynamically. The experimental feasibility of this scheme is analyzed, as well as the method to produce the NOON states of phonon modes is presented using the generated multiparticle entangled states. This scheme may have interesting applications for quantum information processing.

Topological quantum transport and spatial entanglement distribution via a disordered bulk channel

We show how to implement quantum transport, generate entangled state and achieve spatial entanglement distribution via topological Thouless pumping in one-dimensional disordered lattices. We introduce the on-site disorders to suppress the high-order resonant tunneling (which cause wavepacket dispersion) and realize dispersionless Thouless pumping. The interplay between the on-site disorders and the band topology enables robust unidirectional transport. We also demonstrate how to prepare spatially entangled two-particle NOON state via Hong-Ou-Mandel interference assisted by the Thouless pumping. The quantum entanglement can be well preserved during the distribution between spatially separated sites. Our system paves a way to wide applications of topology in quantum information process.

Hybrid Quantum Computing with Conditional Beam Splitter Gate in Trapped Ion System.

The hybrid approach to quantum computation simultaneously utilizes both discrete and continuous variables, which offers the advantage of higher density encoding and processing powers for the same physical resources. Trapped ions, with discrete internal states and motional modes that can be described by continuous variables in an infinite-dimensional Hilbert space, offer a natural platform for this approach. A nonlinear gate for universal quantum computing can be implemented with the conditional beam splitter Hamiltonian |e⟩⟨e|(a[over ^]^{†}b[over ^]+a[over ^]b[over ^]^{†}) that swaps the quantum states of two motional modes, depending on the ion's internal state. We realize such a gate and demonstrate its applications for quantum state overlap measurements, single-shot parity measurement, and generation of NOON states.

Effect of Inter-Well Interactions on Non-Linear Beam Splitters for Matter-Wave Interferometers

We study the non-linear beam splitter in matter-wave interferometers using ultracold quantum gases in a double-well configuration in presence of non-local interactions inducing inter-well density-density coupling, as they can be realized, e.g., with dipolar gases. We explore this effect after considering different input states, in the form of either coherent, or Twin-Fock, or NOON states. We first review the non-interacting limit and the case in which only the local interaction is present, including the study of sensitivity near the self-trapping threshold. Then, we consider the two-mode model in the presence of inter-well interactions and consider the scaling of the sensitivity as a function of the non-local coupling strength. Our analysis clearly shows that non-local interactions can compensate the degradation of the sensitivity induced by local interactions, so that they may be used to restore optimal sensitivity.

Generating NOON states in circuit QED using a multiphoton resonance in the presence of counter-rotating interactions

The NOON states are valuable quantum resources, which have a wide range of applications in quantum communication, quantum metrology, and quantum information processing. Here we propose a fast, concise and reliable protocol for deterministically generating the NOON states of two resonators coupled to a single $\triangle$-type superconducting qutrit. In particular, we derive the effective Hamiltonians at the multi-photon resonances by virtue of the strong counter-rotating interaction between the resonator modes and the qutrit. Based on these crucial effective Hamiltonians, our protocol simplifies the previous ones using the single-photon resonance and consequently reduces the number of operations for state preparation. To test the robustness of this protocol, we analyze the effects from both the decoherence including dissipation and dephasing and the crosstalk of resonator modes on the state fidelity through a Lindblad master equation in the eigenstates of the full Hamiltonian.

Pancharatnam-Berry geometric phase memory based on spontaneous parametric down-conversion.

Phase memory is an effect in which the interaction between a coherent pump beam and a nonlinear crystal generates photon pairs via the spontaneous parametric down-conversion process, then the down-converted photons (signal and idler) can carry the phase information of the pump beam. There has been much research on the memory of the dynamic phase so far; however, there is no report on the memory of non-dynamic phase, to the best of our knowledge. Here we acquire a Pancharatnam-Berry (PB) geometric phase in a physical system when light travels along a trajectory in polarization-state space. Induced coherence occurs in a cascaded scheme composed of two nonlinear crystals, when the idler photons in both crystals are aligned to be indistinguishable. A NOON ($N\; = \;{2}$N=2) state is established when blocking the two idler photons. We explore the PB geometric phase memory of the NOON state and induced coherence. We find that the first-order interference of the two-photon state or signal photons can be controlled by introducing the PB geometric phase to the pump light. This may facilitate precise control of the phase of the down-converted photons.

Deterministic generation of hybrid high- N NOON states with Rydberg atoms trapped in microwave cavities

Trapped ions are among the most promising platforms for quantum technologies. They are at the heart of the most precise clocks and sensors developed to date, which exploit the quantum coherence of a single electronic or motional degree of freedom of an ion. However, future high precision quantum metrology will require the use of entangled states of several degrees of freedom. Here we propose a protocol capable of generating high N00N states where the entanglement is shared between the motion of a trapped ion and an electromagnetic cavity mode, a so called hybrid configuration. We prove the feasibility of the proposal in a platform consisting of a trapped ion excited to its circular Rydberg state manifold, coupled to the modes of a high Q microwave cavity. This compact hybrid architecture has the advantage that it can couple to signals of very different nature, which modify either the ions motion or the cavity modes. Moreover, the exact same setup can be used right after the state preparation phase to implement the interferometer required for quantum metrology.

High-NOON States with High Flux of Photons Using Coherent Beam Stimulated Noncollinear Parametric Down Conversion

We show how to reach high fidelity NOON states with a high count rate inside optical interferometers. Previously, it has been shown that by mixing squeezed and coherent light at a beam splitter, it is possible to generate NOON states of arbitrary N with a fidelity as high as 94%. The scheme is based on higher-order interference between “quantum” down-converted light and “classical” coherent light. However, this requires optimizing the amplitude ratio of classical to quantum light, thereby limiting the overall count rate for the interferometric super-resolution signal. We propose using coherent beam stimulated noncollinear two-mode down-converted light as input to the interferometer. Our scheme is based on the stimulation of noncollinear parametric down conversion by coherent light sources. We get a better flexibility of choosing the amplitude ratio in generating NOON states. This enables super-resolution intensity exceeding the previous scheme by many orders of magnitude. Therefore, we hope to improve the magnitude of N-fold super-resolution in quantum interferometry for arbitrary N using bright light sources. We give improved results for N = 4 and 5.

Criteria to detect macroscopic quantum coherence, macroscopic quantum entanglement, and an Einstein-Podolsky-Rosen paradox for macroscopic superposition states

According to classical theory, a system with two or more macroscopically distinct states available to it is in one of those states at all times. Quantum mechanics gives a different interpretation where the system can be in a superposition of such states. In this paper, we derive criteria in the form of inequalities to detect this effect, referred to as mesoscopic quantum coherence, where the states are (at least) mesoscopically distinct. Such criteria are also signatures of a mesoscopic Schr\odinger cat paradox. We extend the treatment to consider definitions and criteria for mesoscopically entangled states, which are a subset of the states exhibiting mesoscopic quantum coherence. It is shown how the criteria (referred to as type I criteria) can be applied to detect the mesoscopic entanglement of systems prepared in NOON states, Greenberger-Horne-Zeilinger states, and entangled cat states involving coherent states. Here, a larger system $C$ is entangled with a second system $S$, which can be small. The proposed definition of mesoscopic (macroscopic) entanglement involves the Schmidt decomposition, and can be applied to systems in a superposition of many states, only some pairs of which are mesoscopically (macroscopically) distinguishable. We prove that a higher-order Hillery-Zubairy entanglement criterion will detect mesoscopic entanglement of this type, and use this to demonstrate the mesoscopic entanglement of the ground state of a two-mode Bose-Einstein condensate. Finally, we explain how a subset of the type I criteria (called type II criteria) are EPR steering inequalities allowing realization of a mesoscopic or macroscopic version of the Einstein-Podolsky-Rosen paradox for macroscopic superposition states. Where the two systems $C$ and $S$ are spatially separated, we then use results from the literature to point out it is not possible to complete quantum mechanics using hidden-variable theories compatible with the assumption of locality between the two systems. The violation of certain Bell inequalities is sufficient to prove this result, which gives a stricter signature of the Schr\odinger cat paradox and of mesoscopic quantum coherence. We call such signatures type III criteria.

A high-N00N output of harmonically driven cavity QED

A harmonically driven cavity QED system consisting of two cavities and a two-level qubit is shown to enable the generation of a vast class of maximally entangled states suitable for measurements with a Heisenberg-limit precision. As one of its modalities, this system can serve as a quantum beam splitter, converting an |N〉 ⊗ |0〉 input into a maximally entangled N00N state (|N〉 ⊗ |0〉 + |0〉 ⊗ |N〉)/sqrt{{bf{2}}} at its output. A network of such quantum beam splitters is shown to provide a source of multimode N00N-type entanglement.

Coherent perfect absorption of single photons in a fiber network

Large distance implementation of quantum communication technologies requires coherent control of single photons in optical fiber networks. Here we demonstrate the phenomenon of coherent perfect absorption of single photons in a fully fiberized ultrathin plasmonic metamaterial fabricated at the end facet of an optical fiber. Continuous control of single-photon absorption probability is achieved by driving the network between the regimes of coherent total absorption and coherent total transmission. To circumvent phase fluctuations inherent to optical fiber networks, we implemented a reference-based postselection technique which yielded interference fringe visibility comparable to that of free space experiments. Coherent absorption of quantum light in fiber environment provides new opportunities for dissipative single-photon switching, filtering, and measurement, as well as for manipulation of entangled, weak coherent, and NOON states in optical fiber networks.

Conversion of Gaussian states to non-Gaussian states using photon-number-resolving detectors

Generation of high fidelity photonic non-Gaussian states is a crucial ingredient for universal quantum computation using continous-variable platforms, yet it remains a challenge to do so efficiently. We present a general framework for a probabilistic production of multimode non-Gaussian states by measuring few modes of multimode Gaussian states via photon-number-resolving detectors. We use Gaussian elements consisting of squeezed displaced vacuum states and interferometers, the only non-Gaussian elements consisting of photon-number-resolving detectors. We derive analytic expressions for the output Wigner function, and the probability of generating the states in terms of the mean and the covariance matrix of the Gaussian state and the photon detection pattern. We find that the output states can be written as a Fock basis superposition state followed by a Gaussian gate, and we derive explicit expressions for these parameters. These analytic expressions show exactly what non-Gaussian states can be generated by this probabilistic scheme. Further, it provides a method to search for the Gaussian circuit and measurement pattern that produces a target non-Gaussian state with optimal fidelity and success probability. We present specific examples such as the generation of cat states, ON states, Gottesman-Kitaev-Preskill states, NOON states and bosonic code states. The proposed framework has potential far-reaching implications for the generation of bosonic error-correction codes that require non-Gaussian states, resource states for the implementation of non-Gaussian gates needed for universal quantum computation, among other applications requiring non-Gaussianity. The tools developed here could also prove useful for the quantum resource theory of non-Gaussianity.

Generation of NOON States in Waveguide Arrays

AbstractA method to generate NOON states with three photons by injecting photons in an array of three waveguides is presented. Conditional measurements project the wave function in a given (desired) state. In passing, it is shown how the array of three waveguides, that effectively reproduces the interaction of three fields, may be reduced to the interaction of two fields.

Sorting-based approach to multiphoton interference.

Multiphoton interference is an essential component of quantum technologies such as quantum computation, quantum communication, and quantum metrology. We introduce a sorting-based approach to multiphoton interference and examine its implications for quantum metrology and teleportation. Our examination reveals an extension of the seminal Hong-Ou-Mandel effect whose resultant state is the highly desired multiphoton NOON state. Application of the above perspective to entangled photons reveals a novel approach to quantum qudit teleportation.

Metasurface interferometry toward quantum sensors

Optical metasurfaces open new avenues for the precise wavefront control of light for integrated quantum technology. Here, we demonstrate a hybrid integrated quantum photonic system that is capable of entangling and disentangling two-photon spin states at a dielectric metasurface. Via the interference of single-photon pairs at a nanostructured dielectric metasurface, a path-entangled two-photon NOON state with circular polarization that exhibits a quantum HOM interference visibility of 86 ± 4% is generated. Furthermore, we demonstrate nonclassicality andphase sensitivity in a metasurface-based interferometer with a fringe visibility of 86.8 ± 1.1% in the coincidence counts. This high visibility proves the metasurface-induced path entanglement inside the interferometer. Our findings provide a promising way to develop hybrid-integrated quantum technology operating in the high-dimensional mode space in various applications, such as imaging, sensing, and computing.

Experimental implementation of an NMR NOON state thermometer

Utilizing the highly correlated quantum NOON states of spins, we have implemented a proof-of-principle quantum thermometer using the NMR technique for measuring the variation of local magnetic field with the temperature. The system used was the star topology system of hexafluorophosphate molecules, and the thermometer showed a sensitivity of $$85\,\mathrm{nT}/^\circ $$ C. Using the hexafluorophosphate and the trimethylphosphite spin systems, we have quantified the advantage of the quantum protocol over the classical one for measuring magnetic field. The quantum protocol showed the best performance for the sensing time of $$T_\mathrm{max} = 20\,$$ ms, where the errors in the measurement scaled as the Heisenberg limit 1 / N. The thermometer implementation provided measurements in the temperature with errors scaling approximately with the Heisenberg limit, more precisely $$N^{-0.94}$$ .

Efficient methods for generating multi-mode NOON states

Two experimental setups to generate multi-mode NOON states are proposed. The first setup is a universal model, which can create a d-mode N-photon NOON state with an arbitrary mode number d and photon number N in principle in a lossless system with perfect optical devices, using states with non-deterministic distributions of photons as the input sources and post-selection of total N photons for detection. The second approach, on the other hand, can generate a 4-mode 4-photon NOON state using single photon sources. The core unit of both setups is the Fock state filter, which is used to filter out an arbitrary Fock state component from an incident state using a beam splitter with proper transmissivity. The intrinsic generation efficiencies of the NOON states produced by both methods, with the first setup particularly focused on using squeezed vacuum states as the inputs, are calculated. They are found to be at least two orders of magnitude larger than and scale more favorably to the previously proposed approach using coherent state inputs. We also show that the second setup has the best performance for the case with d=N=4, while the first method scales better for a larger N or d. These results manifest that multi-mode NOON states with 3 or 4 modes and 4 or 6 photons could feasibly be generated in experiments with current photonic technologies.

Enhancing test precision for local Lorentz-symmetry violation with entanglement

A recent proposal for testing Lorentz-symmetry violation (LSV) presents a formulation where the effect of violation is described as a local interaction [R. Shaniv et al., Phys. Rev. Lett. 120, 103202 (2018)]. An entangled ion pair in a decoherence free subspace (DFS) is shown to double the signal-to-noise ratio (SNR) of one ion, while (even)-$N/2$ such DFS pairs in a collective entangled state improve SNR by $N$ times, provided the state parity or the even or odd numbers of ions can be measured. It remains to find out, however, how such fiducial entangled states can be prepared at nonexponentially small success rates. This work suggests two types of many-particle entangled states for testing LSV: the maximally entangled NOON state, which can achieve Heisenberg limited precision; and the balanced spin-1 Dicke state, which is readily available in deterministic fashion. We show that the latter also lives in a DFS and is immune to stray magnetic fields. It can achieve classical precision limit or the standard quantum limit (SQL) based on collective population measurement without individual atom resolution. Given the high interests in LSV and in entanglement assisted quantum metrology, our observation offers additional incentives for pursuing practical applications of many-atom entangled states.

Generation of two-photon noon state and polarization-entangled state from a single quantum dot embedded inside a microcavity

We discuss generation of two types of entangled states of two photons: noon state, which is entangled in number and polarization, and polarization-entangled state, which is entangled in polarization and frequency. We consider a single quantum dot coupled with a bimodal cavity in a strong coupling regime. We analyze the effect of exciton–phonon coupling on concurrence of the generated entangled states. We find that for both states, concurrence is maximum in the absence of an anisotropic energy gap between exciton states and remains unchanged in the presence of exciton–phonon coupling. However, for finite anisotropic, energy gap concurrence decreases with increasing temperature of the phonon bath.

Disorder-Robust Entanglement Transport.

We study the disorder-perturbed transport of two noninteracting entangled particles in the absence of backscattering. This situation is, for instance, realized along edges of topological insulators. We find profoundly different responses to disorder-induced dephasing for the center-of-mass and relative coordinates: While a mirror symmetry protects even highly delocalized relative states when resonant with the symmetry condition, delocalizations in the center of mass [e.g., two-particle (N=2) N00N states] remain fully sensitive to disorder. We demonstrate the relevance of these differences to the example of interferometric entanglement detection. Our platform-independent analysis is based on the treatment of disorder-averaged quantum systems with quantum master equations.