cross-Kerr Nonlinearity Research Articles

Filtration mapping as complete Bell state analyzer for bosonic particles

In this paper, we present the approach to complete Bell state analysis based on filtering mapping. The key distinctive feature of this appoach is that it avoids complications related to using either hyperentanglement or representation of the Bell states as concatenated Greenber–Horne–Zeilinger (C-GHZ) state to perform discrimination procedure. We describe two techniques developed within the suggested approach and based on two-step algorithms with two different types of filtration mapping which can be called the non-demolition and semi-demolition filtrations. In the method involving non-demolition filtration measurement the filtration process employs cross-Kerr nonlinearity and the probe mode to distinguish between the two pairs of the Bell states. In the case of semi-demolition measurement, the two states are unambiguously discriminated and hence destroyed, whereas filtraton keeps the other two states intact. We show that the measurement that destroys the single photon subspace in every mode and preserves the superposition of zero and two photons can be realized with discrete photodetection based on microresonator with atoms.

Procedure via cross-Kerr nonlinearities for encoding single logical qubit information onto four-photon decoherence-free states

We propose a photonic procedure using cross-Kerr nonlinearities (XKNLs) to encode single logical qubit information onto four-photon decoherence-free states. In quantum information processing, a decoherence-free subspace can secure quantum information against collective decoherence. Therefore, we design a procedure employing nonlinear optical gates, which are composed of XKNLs, quantum bus beams, and photon-number-resolving measurements with linear optical devices, to conserve quantum information by encoding quantum information onto four-photon decoherence-free states (single logical qubit information). Based on our analysis in quantifying the affection (photon loss and dephasing) of the decoherence effect, we demonstrate the experimental condition to acquire the reliable procedure of single logical qubit information having the robustness against the decoherence effect.

Entanglement concentration for six-particle cluster states

Multi-particle cluster states play a significant role in quantum information processing. However, due to the inevitable interaction with the environment in the transmission process, the fidelity of entanglement decreases. To distill the perfect cluster states, we present two schemes for arbitrary six-particle cluster states. POVM local unitary operators that are obtained by solving the equation according to the properties of cluster states are used in the first protocol. The second protocol is based on cross-Kerr nonlinearity which is exploited to check parity between original qubit with ancillary single qubit and it can achieve a higher probability of success through iteration. Furthermore, we can generalize the first method to concentrate entanglement on even number of particles. Our protocol will be useful in practical applications.

One-step direct measurement of the entangled W states with cross-Kerr nonlinearity

We propose a scheme to directly measure the entangled W states with cross-Kerr nonlinearity mediums. This scheme can measure three-photon, four-photon, and even N-photon W states in one step. Only PBSs and cross-Kerr nonlinearity mediums are used in this scheme, which is feasible for experiments. We describe the three-photon W states measurement process and extend it to four-photon and N-photon W states.

Giant Kerr nonlinearities and magneto-optical rotations in a Rydberg-atom gas via double electromagnetically induced transparency

We investigate the Kerr and magneto-optical effects for a probe laser field with two orthogonally polarized components, propagating in a cold Rydberg atomic gas with an inverted-Y-type level configuration via double electromagnetically induced transparency (EIT). Through an approach beyond both mean-field and ground-state approximations, we make detailed calculations on third-order nonlinear optical susceptibilities and show that the system possesses giant nonlocal selfand cross-Kerr nonlinearities contributed by Rydberg-Rydberg interaction. The theoretical result of the cross-Kerr nonlinearity obtained for 85Rb atomic gas is very close to the experimental one reported recently. Moreover, we demonstrate that the probe laser field can acquire a very large magnetooptical rotation via the double EIT, which may be used to design atomic magnetometers with high precision. The results presented here are promising not only for the development of nonlocal nonlinear magneto-optics but also for applications in precision measurement and optical information processing and transmission based on Rydberg atomic gases.

Logic W‐state concentration with parity check

Logic W state, which replaces each physical qubit in a W state with a Greenberger–Horne–Zeilinger state is robust against photon transmission loss in long-distance quantum communication. In practical application, the environmental noise may make maximally entangled logic W state degrade to less entangled state, which largely limits its application. In this article, we propose an efficient entanglement concentration protocol (ECP) for logic W state, which can recover the less entangled logic W state into the maximally entangled logic W state. Our ECP relies on the nondemolition polarization parity check (PPC) gate constructed with cross-Kerr nonlinearity. The distilled maximally entangled logic W state can be preserved for other application. Moreover, when the ECP fails, we can repeat the ECP to further concentrate the distilled less entangled logic W state. By repeating the ECP, the total success probability can be effectively increased. Based on above features, this ECP may be useful in quantum communication field.

Giant cross-Kerr nonlinearity in a four-level Y-type atomic system

The analytical expression for the group index in a degenerated three-level lambda-type atomic system is derived as a function of the parameters of laser fields and external magnetic field. The influence of the external magnetic field on the group index is investigated. It is shown that by changing the magnitude or sign of the external magnetic field, the transparency window with normal dispersion switches to enhanced absorption with anomalous dispersion at the line center and hence the light propagation can be converted between subluminal and superluminal modes. Full Text: PDF ReferencesR. W. Boyd, "Slow and fast light: fundamentals and applications", J. Mod. Opt. 56 (2009) 1908-1915 CrossRef K.J. Boller, A. Imamoglu, S.E. Harris, "Observation of electromagnetically induced transparency", Phys. Rev. Lett. 66 (1991) 2593. CrossRef A. Lezama, S. Barreiro, and A. M. Akulshin, "Electromagnetically induced absorption", Phys. Rev. A 59 (1999) 4732-4735. CrossRef L. V. Hau, S. E. Harris, Z. Dutton, C. H. Bejroozi, "Light speed reduction to 17 metres per second in an ultracold atomic gas", Nature 397, 594 (1999) CrossRef L. J. Wang, A. Kuzmich, and A. Dogariu, "Gain-assisted superluminal light propagation", Nature 406 (6793), 277-279 (2000) CrossRef A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hammer, "Observation of Ultraslow and Stored Light Pulses in a Solid", Phys. Rev. Lett. 88, 023602 (2002). CrossRef K. Bencheikh, E. Baldit, S. Briaudeau, P. Monnier, J. A. Levenson, and G. Mélin, "Slow light propagation in a ring erbium-doped fiber", Opt. Express 18 (25), 25642-25648 (2010). CrossRef E. E. Mikhailov, V. A. Sautenkov, I. Novikova, G. R. Welch, "Large negative and positive delay of optical pulses in coherently prepared dense Rb vapor with buffer gas", Phys. Rev. A 69, 063808 (2004). CrossRef E. E. Mikhailov, V. A. Sautenkov, Y. V. Rostovtsev, G.R. Welch, "Absorption resonance and large negative delay in rubidium vapor with a buffer gas", J. Opt. Soc. Am. B 21, 425 (2004). CrossRef A. M Akulshin and R. J McLean, "Fast light in atomic media", J. Opt. 12 (2010) 104001. CrossRef Vineet Bharti, Vasant Natarajan, "Sub- and super-luminal light propagation using a Rydberg state", Opt. Comm. 392 (2017) 180-184. CrossRef N.T. Anh, L.V. Doai, D.H. Son, and N.H. Bang, "Manipulating multi-frequency light in a five-level cascade EIT medium under Doppler broadening", Optik 171 (2018) 721-727. CrossRef N.T. Anh, L.V. Doai, and N.H. Bang, "Manipulating multi-frequency light in a five-level cascade-type atomic medium associated with giant self-Kerr nonlinearity", J. Opt. Soc. Am. B 35 (2018) 1233. CrossRef N.H. Bang, L.N.M. Anh, N.T. Dung and L.V. Doai, "Comparative Study of Light Manipulation in Three-Level Systems Via Spontaneously Generated Coherence and Relative Phase of Laser Fields*", Commun. Theor. Phys. 71 (2019) 947-954. CrossRef L.V. Doai, "The effect of giant Kerr nonlinearity on group velocity in a six-level inverted-Y atomic system", Physica Scripta 95 (2020) 035104 (7pp). CrossRef P. Kaur and A. Wasan, "Effect of magnetic field on the optical properties of an inhomogeneously broadened multilevel Λ-system in Rb vapor", Eur. Phys. J. D 71 (2017) 78. CrossRef H. Cheng, H. -M. Wang, S. -S. Zhang, P. -P. Xin, J. Luo and H. -P. Liu, "Electromagnetically induced transparency of 87Rb in a buffer gas cell with magnetic field", J. Phys. B: At. Mol. Opt. Phys. 50 (2017) 095401. CrossRef C. Mishra, A. Chakraborty, A. Srivastava, S. K. Tiwari, S. P. Ram, V. B. Tiwari and S. R. Mishr, "lectromagnetically induced transparency in Λ-systems of 87Rb atom in magnetic field", J. Mod. Opt. 65 (2018) 2269-2277. CrossRef S. H. Asadpour, H. R. Hamedi and H. R. Soleimani, "Slow light propagation and bistable switching in a graphene under an external magnetic field", Laser Phys. Lett. 12 (2015) 045202. CrossRef R. Karimi, S. H. Asadpour, S. Batebi and h. R. Soleimani, "Manipulation of pulse propagation in a four-level quantum system via an elliptically polarized light in the presence of external magnetic field", Mod. Phys. Lett. B 29 (2015) 1550185. CrossRef

One-step Realization of a Cross-Kerr Nonlinearity Between Two Ensembles of NV Centers via a Superconducting Flux Qubit

Cross-Kerr nonlinearity has many important applications in quantum computation and quantum information processing. Here, we propose a one-step method to realize a cross-Kerr nonlinearity between two nitrogen-vacancy center ensembles (NV ensembles). The realization of cross-Kerr nonlinearity is based on a superconducting flux qubit dispersively coupled to two NV ensembles. Numerical simulations show that this cross-Kerr nonlinearity can be high-fidelity constructed a two-qubit controlled phase gate of NV ensembles.

Fluctuation-enhanced Kerr nonlinearity in an atom-assisted optomechanical system with atom-cavity interactions.

We examine the effect of cavity field fluctuations on Kerr nonlinearity in an atom-assisted optomechanical system. It is found that a new self-Kerr (SK) nonlinearity term, which can greatly surpass that of a classical Λ type atomic system when the hybrid system has numerous atoms, is generated based on cavity field fluctuations by atom-cavity interactions. A strong photon-phonon cross-Kerr (CK) nonlinearity is also produced based on cavity field fluctuations. These nonlinearity features can be modified by atom-cavity and optomechanical interactions. This work may provide a new method to enhance the SK nonlinearity and generate the photon-phonon CK nonlinearity.

Enhanced cross-Kerr nonlinearity induced -symmetry in optical lattices

We propose a physical scheme to realize optical lattices that are symmetric under a combination of parity and time () reversal. The -symmetric structures can be constructed with periodical gain and loss profiles in a coherently prepared four-level N-type atomic system under the effects of cross-Kerr nonlinearity and Doppler broadening. The atoms are considered in the Gaussian density distribution loaded into the dipole traps of one- and two-dimensional optical lattices. The spatial modulation of the probe field susceptibility is achieved by a proper combination of standing wave strong control fields. With proper detunings and coupling field Rabi frequencies, we find the conditions of achieving -symmetry in optical lattices of nonlinear atoms. We show that the -symmetry can be realized when the cross-Kerr nonlinearity is significantly enhanced, and further demonstrate that it survives the Doppler broadening. Our model is based on experimentally observable and effectively controllable scheme which may find potential applications in optical information processing.

Deterministic nondestructive state analysis for polarization-spatial-time-bin hyperentanglement with cross-Kerr nonlinearity* *Project supported by the National Natural Science Foundation of China (Grant No. 11604226) and Science and Technology Program Foundation of the Beijing Municipal Commission of Education of China (Grants No. CIT&TCD201904080).

We present a deterministic nondestructive hyperentangled Bell state analysis protocol for photons entangled in three degrees of freedom (DOFs), including polarization, spatial-mode, and time-bin DOFs. The polarization Bell state analyzer and spatial-mode Bell state analyzer are constructed by polarization parity-check quantum nondemolition detector (P-QND) and spatial-mode parity-check quantum nondemolition detector (S-QND) using cross-Kerr nonlinearity, respectively. The time-bin Bell state analyzer is constructed by the swap gate for polarization state and time-bin state of a photon (P-T swap gate) and P-QND. The Bell states analyzer for one DOF will not destruct the Bell states of other two DOFs, so the polarization-spatial-time-bin hyperentangled Bell states can be determinately distinguished without destruction. This deterministic nondestructive state analysis method has useful applications in quantum information protocols.

Hyperentanglement concentration of nonlocal two-photon six-qubit systems via the cross-Kerr nonlinearity

We present an efficient hyperentanglement concentration protocol (hyper-ECP) for two-photon six-qubit systems in nonlocal partially hyperentangled Bell states with unknown parameters. In our scheme, we use two identical partially hyperentangled states which are simultaneously entangled in polarization and two different longitudinal momentum degrees of freedom (DOFs) to distill the maximally hyperentangled Bell state. The quantum nondemolition detectors based on the cross-Kerr nonlinearity are used to realize the parity checks of two-photon systems in three DOFs. The hyper-ECP can extract all the useful entanglement source, and the success probability can reach the theory limit with the help of iteration. All these advantages make our hyper-ECP useful in long-distance quantum communication in the future.

Enhancing optical delay using cross-Kerr nonlinearity in Rydberg atoms.

A scheme to enhance the optical delay in Rydberg atoms is proposed. In the linear case, the optical delay in a four-level system can be significantly enhanced compared to that of the three-level system. However, the width of the transparent window will decrease with an increase in the optical delay. In the nonlinear case, the nonlinear dispersion becomes steep around the transparency window. The enhanced cross-Kerr nonlinearity mainly contributes to the effective dispersion, which dramatically increases the optical delay. The simulation result shows that the optical delay of the system could be enhanced tens of times; moreover, the wide transparency window remains. So the delay-bandwidth product could be significantly improved due to nonlinear dispersion. We further examine Gaussian pulse propagation in the Rydberg atoms.

Scheme for Bidirectional Quantum Teleportation of Unknown Electron-Spin States of Quantum Dots within Single-Sided Cavities

We represent the mutual swapping of two unknown states using bidirectional quantum teleportation (BQT) while transferring a single photon. In our BQT scheme, two users (Alice and Bob) can mutually teleport their two unknown states of the electron-spin in quantum dots (QDs) embedded in single-sided cavities. For this BQT scheme, we employ the interactions of a photonic spin (photon) and an electron-spin (excess electron) of QDs confined in a single-sided cavity, which is feasible in practice. The previous BQT scheme which used cross-Kerr nonlinearities (XKNLs) and X-homodyne detection was inevitable the decoherence effect in optical fibers. Consequently, the proposed BQT scheme can enhance an experimental implementation with the use of QD-cavity systems under the decoherence effect and this can also be realized with current technology, compared with the previous BQT scheme based on XKNLs.

Generation of an arbitrary logic W state with cross-Kerr nonlinearities

Environmental noise is a big obstacle in quantum communication and computation. Quantum error code (QEC) technology can resist the photon transmission loss and decoherence error caused by the environmental noise and has great application potential in future quantum communication and computation fields. The generation of logic qubits or logic entanglement is the important first step of the QEC. The logic W state, which replaces each physical qubit in a physical W state with a logic qubit, may be highly robust against photon loss and errors, so that it may have big application potential. In this paper, we propose an efficient scheme to generate an arbitrary logic W state with the help of cross-Kerr nonlinearities. Our protocol only requires a physical W state and some auxiliary single photons, and can deterministically generate a general logic W state based on the homodyne measurement results. Our logic W state generation protocol may be useful in future quantum information processing based on the logic W state.

Tunneling-induced optical limiting in quantum dot molecules

We present a convenient way to obtain an optical power limiting behavior in a quantum dot molecule system, induced by an interdot tunneling. Also, the effect of system parameters on the limiting performance is investigated; interestingly, the tunneling rate can affect the limiting performance of the system so that the threshold of the limiting behavior can be a function of the input voltage, allowing the optimization of the limiting action. Furthermore, by investigating the absorption of the probe field, it is demonstrated that the optical limiting is due to a reverse saturable absorption mechanism; indeed, analytical results show that this mechanism is based on a cross-Kerr optical nonlinearity induced by the tunneling. Additionally, the limiting properties of the system are studied by using a Z-scan technique.

Experimental demonstration of cavity-free optical isolators and optical circulators

Cavity-free optical nonreciprocity components, which have an inherent strong asymmetric interaction between the forward- and backward-propagation direction of the probe field, are key to produce such as optical isolators and circulators. According to the proposal presented by Xia et al., [Phys. Rev. Lett. 121, 203602 (2018)], we experimentally build a device that uses cross-Kerr nonlinearity to achieve a cavity-free optical isolator and circulator. Its nonreciprocal behavior arises from the thermal motion of N-type configuration atoms, which induces a strong chiral cross-Kerr nonlinear response for the weak probe beam. We obtain a two-port optical isolator for up to 20 dB of isolation ratio in a specially designed Sagnac interferometer. The distinct propagation directions of the weak probe field determine its cross-phase shift and transmission, by which we demonstrate the accessibility of a four-port optical circulator.

Semi-quantum key distribution protocol based on the hyperentanglement Bell state of polarization-spatial mode

The semi-quantum key distribution protocol based on the hyperentanglement Bell state of polarization-spatial mode is presented in this paper. This protocol is utilized to share the session keys and construct key hierarchy of security systems in high capacity between the legitimate users securely. Different from the previous protocols, two quantum non-demolition detectors are constructed with cross-Kerr nonlinearities and different phase shifts for distinguishing the Bell states in spatial mode degree of freedom. Meanwhile, this protocol can improve the capacity and efficiency when the legitimate users share the session keys. And the technology of the hyperentanglement purification and hyperentanglement concentration can enhance the robustness and stability of this protocol. At last, this protocol proposed in this paper can withstand several kinds of attacks.

Complete hyperentangled state analysis using weak cross-Kerr nonlinearity and auxiliary entanglement

We present a new method for the complete analysis of hyperentangled Bell state and Greenberger–Horne–Zeilinger state in polarization and spatial-mode degrees of freedom, resorting to weak cross-Kerr nonlinearity and auxiliary frequency entanglement. The weak cross-Kerr nonlinearity with small phase shift is used to construct quantum nondestructive detector, and it is realizable with the current technology. Compared with the previous schemes, our scheme largely reduces the requirement on nonlinearity with the help of auxiliary entanglement in the third degree of freedom. Our method provides an efficient avenue for the hyperentangled state analysis, and will be useful for high-capacity quantum information processing.

Generation of two-photon hybrid-entangled W state with photonic qubit and time-bin via cross-Kerr nonlinearities

Herein, we present a scheme to prepare a hybrid-entangled W state that possesses the polarization states of two photons and the time-bin using cross-Kerr nonlinearities (XKNLs) and linearly optical devices. To maximize the merit of the entangled W state that can conserve entanglement against the loss of one qubit, we propose a method to prepare a two-photon hybrid-entangled W state correlated with degrees of freedom (polarization and the time-bin) via nonlinearly optical gates using XKNLs. In our scheme, the nonlinear gates consist of weak XKNLs, quantum bus beams, and photon-number-resolving measurements to realize the controlled-path gate and merging-path gate between two photons. To insert the time-bin information into photons, the time-bin encoder employs only linearly optical devices (delay lines and polarizing beam splitters). Subsequently, to evaluate the efficiency and experimental feasibility of our scheme for generating a two-photon hybrid-entangled W state, we analyzed the performance of nonlinear gates using XKNLs under the decoherence effect.