Cascaded Four-wave Mixing Processes Research Articles

Enhancement of quadripartite quantum correlation via phase-sensitive cascaded four-wave mixing process

Multipartite quantum correlation is important for both fundamental science and quantum information processing. Its enhancement is critical to improve the performance of physical systems. Therefore, it is of great practical significance to study the enhancement of multipartite quantum correlation. Here, we theoretically investigate a scheme for enhancing quadripartite quantum correlation by utilizing a phase-sensitive cascaded four-wave mixing (CFWM) process. We find that the intensity-difference squeezing (IDS) among the four output beams generated by the phase-insensitive CFWM process can be largely enhanced by introducing the phase-sensitive CFWM process. We also find that our phase-sensitive CFWM process can be used to generate intensity-sum squeezing (ISS), which cannot be generated by the phase-insensitive CFWM process. Moreover, we find that the maximum squeezing value of ISS is equal to that of IDS when the intensity gains of the three four-wave mixing processes are equal in the phase-sensitive cascaded scheme. In the end, we discuss the effects of the losses and the phase fluctuations on the squeezing values of our phase-sensitive CFWM process and the corresponding phase-insensitive CFWM process with the same intensity gains. It can be seen that the squeezing enhancement of our phase-sensitive CFWM process holds also in presence of the losses and the phase fluctuations. Our results pave the way for experimental implementation and may find applications in quantum metrology and quantum communication.

Multi-Way Noiseless Signal Amplification in a Symmetrical Cascaded Four-Wave Mixing Process

According to the fundamental laws of quantum optics, vacuum noise is inevitably added to the signal when one tries to amplify a signal. However, it has been recently shown that noiseless signal amplification can be realized when a phase-sensitive process is involved. Two phase-sensitive schemes, a correlation injection scheme and a two-beam phase-sensitive amplifier scheme, are both proposed to realize multi-way noiseless signal amplification in a symmetrical cascaded four-wave mixing process. We theoretically study the possibility of the realization of four-way noiseless signal amplification by using these two schemes. The results show that the correlation injection scheme can only realize one-way noiseless signal amplification, but that the two-beam phase-sensitive amplifier scheme can lead to four-way noise figure values below 1. Our results here may find potential applications in quantum information processing, e.g., the realization of quantum information tap and quantum non-demolition measurement, etc.

Generation of octapartite entanglement by connecting two symmetric cascaded four-wave mixing processes with one linear beam splitter

We theoretically propose a scheme for generating full octapartite entanglement using two symmetric cascaded four-wave mixing (FWM) processes and one linear beam splitter (BS), in which two independent symmetric cascaded FWM processes are connected by a BS. To present the entanglement properties of the system, we first verify that the generated state is a H -graph state by exploiting the graphical calculus for Gaussian pure states, and reveal the internal interaction of the generated state by using the derived coupling strength matrix. We proceed with investigating the possibility of this scheme for generating octapartite entanglement by applying the positivity under a partial transposition criterion. The results show that there exists full octapartite entanglement in the whole gain region, and the degree of entanglement increases as the power gain increases. In addition, we investigate the effect of transmissivity of BS on the entanglement properties of the system and the dependence of bipartite entanglement on the power gain and the transmissivity of BS. Our results give a simple way to increase the scale of entanglement by linear optics and cascaded FWM processes.

Ultrafast 1 MHz vacuum-ultraviolet source via highly cascaded harmonic generation in negative-curvature hollow-core fibers

Vacuum-ultraviolet (VUV) light is critical for the study of molecules and materials, but the generation of femtosecond pulses in the VUV region at high repetition rates has proven difficult. Here we demonstrate the efficient generation of VUV light at megahertz repetition rates using highly cascaded four-wave mixing processes in a negative-curvature hollow-core fiber. Both even- and odd-order harmonics are generated up to the 15th harmonic (69 nm, 18.0 eV), with high energy resolution of ∼ 40 m e V . In contrast to direct high harmonic generation, this highly cascaded harmonic generation process requires lower peak intensity and therefore can operate at higher repetition rates, driven by a robust ∼ 10 W fiber-laser system in a compact setup. Additionally, we present numerical simulations that explore the fundamental capabilities and spatiotemporal dynamics of highly cascaded harmonic generation. This VUV source can enhance the capabilities of spectroscopies of molecular and quantum materials, such as photoionization mass spectrometry and time-, angle-, and spin-resolved photoemission.

Multicolor concentric annular ultrafast vector beams.

Novel multicolor concentric annular ultrafast vector beams (MUCAU-VB) are firstly generated simply by using cascaded four-wave mixing (CFWM) in a glass plate pumped by two intense vector femtosecond pulses. A proof-of-principle experiment shows that up to 10 frequency up-conversion concentric annular radially polarized sidebands are obtained simultaneously based on CFWM process, where the spectra range of the first 7 order sidebands extending from 545 nm to 725 nm. The results prove the polarization transfer property from the pump beam to the signal beams even in the CFWM, a third-order optical parametric process. The pulse duration of the first order sideband is measured to be 74 fs which is according with those of two input beams. These novel MUCAU-VB, which are manipulated in temporal, spectral, spatial domain and polarization state simultaneously, are expected to apply in wide fields, such as manipulating particles and multicolor pump-probe experiments.

Tripartite Einstein-Podolsky-Rosen steering with linear and nonlinear beamsplitters in four-wave mixing of Rubidium atoms.

Multipartite Einstein-Podolsky-Rosen (EPR) steering is an essential resource for secure one-sided device-independent quantum secret sharing. Here, we analyze the EPR steering properties exhibited in three-mode Gaussian states created by four-wave mixing (FWM) in Rubidium atoms combined with a linear beamsplitter and a nonlinear beamsplitter (second FWM), respectively. By quantifying Gaussian steerability based on a measure determined by the covariance matrix of the produced states, we compare the performance of two schemes to achieve one-way, collective, and genuine tripartite steering, as well as the monogamy constraints for distributing steering among three parties. We show that the scheme with nonlinear beamsplitter is feasible to create stronger bipartite steering and genuine tripartite steering and has more flexibility to manipulate the monogamy relation through the cooperation of the two cascaded FWM processes.

Experimental characterization of pairwise correlations from quadruple quantum correlated beams generated by cascaded four-wave mixing processes

We theoretically calculate and experimentally investigate the performance of the pairwise correlations from quadruple quantum correlated beams based on the cascaded four-wave mixing (FWM) processes. The experimental results have similar trends to their theoretical predictions. By properly changing the intensity gains of the cascaded FWM processes, we can gradually convert some pairs of classical correlated beams into quantum correlated beams. Our results may find potential applications in the manipulation of quantum correlated beams generated from the cascaded FWM processes.

Experimental characterization of pairwise correlations from triple quantum correlated beams generated by cascaded four-wave mixing processes

We theoretically and experimentally characterize the performance of the pairwise correlations from triple quantum correlated beams based on the cascaded four-wave mixing (FWM) processes. The pairwise correlations between any two of the beams are theoretically calculated and experimentally measured. The experimental and theoretical results are in good agreement. We find that two of the three pairwise correlations can be in the quantum regime. The other pairwise correlation is always in the classical regime. In addition, we also measure the triple-beam correlation which is always in the quantum regime. Such unbalanced and controllable pairwise correlation structures may be taken as advantages in practical quantum communications, for example, hierarchical quantum secret sharing. Our results also open the way for the classification and application of quantum states generated from the cascaded FWM processes.

Generation of quadripartite entanglement from cascaded four-wave-mixing processes

We show that the scheme of cascaded four-wave-mixing (FWM) processes can be a promising alternative method for generating quadripartite entanglement. This scheme utilizes the strongly entangled twin beams produced by a FWM process as seed beams for another two FWM processes. To present the entanglement properties of this scheme, we verify that the generated state is a $\mathcal{H}$-graph state by using the graphical calculus for Gaussian pure states at first. Then we proceed with investigating the possibility of this scheme for generating quadripartite entanglement by applying the positivity under partial transposition criterion. It is verified that quadripartite entanglement exists for the whole gain region in this scheme. In addition, the possibilities of generating bipartite and tripartite entanglement are studied as well to reveal the entanglement structure. Our results pave the way to experimentally generate quadripartite entanglement based on cascaded FWM processes.

Quantum steering in cascaded four-wave mixing processes.

Quantum steering is used to describe the "spooky action-at-a-distance" nonlocality raised in the Einstein-Podolsky-Rosen (EPR) paradox, which is important for understanding entanglement distribution and constructing quantum networks. Here, in this paper, we study an experimentally feasible scheme for generating quantum steering based on cascaded four-wave-mixing (FWM) processes in hot rubidium (Rb) vapor. Quantum steering, including bipartite steering and genuine tripartite steering among the output light fields, is theoretically analyzed. We find the corresponding gain regions in which the bipartite and tripartite steering exist. The results of bipartite steering can be used to establish a hierarchical steering model in which one beam can steer the other two beams in the whole gain region; however, the other two beams cannot steer the first beam simultaneously. Moreover, the other two beams cannot steer with each other in the whole gain region. More importantly, we investigate the gain dependence of the existence of the genuine tripartite steering and we find that the genuine tripartite steering exists in most of the whole gain region in the ideal case. Also we discuss the effect of losses on the genuine tripartite steering. Our results pave the way to experimental demonstration of quantum steering in cascaded FWM process.

Numerical simulation and temporal characterization of dual-pumped microring-resonator-based optical frequency combs

Dual-pumped microring-resonator-based optical frequency combs (OFCs) and their temporal characteristics are numerically investigated and experimentally explored. The calculation results obtained by solving the driven and damped nonlinear Schrodinger equation indicate that an ultralow coupled pump power is required to excite the primary comb modes through a non-degenerate four-wave-mixing (FWM) process and, when the pump power is boosted, both the comb mode intensities and spectral bandwidths increase. At low pump powers, the field intensity profile exhibits a cosine variation manner with frequency equal to the separation of the two pumps, while a roll Turing pattern is formed resulting from the increased comb mode intensities and spectral bandwidths at high pump powers. Meanwhile, we found that the power difference between the two pump fields can be transferred to the newly generated comb modes, which are located on both sides of the pump modes, through a cascaded FWM process. Experimentally, the dual-pumped OFCs were realized by coupling two self-oscillating pump fields into a microring resonator. The numerically calculated comb spectrum is verified by generating an OFC with 2.0 THz mode spacing over 160 nm bandwidth. In addition, the formation of a roll Turing pattern at high pump powers is inferred from the measured autocorrelation trace of a 10 free spectral range (FSR) OFC. The experimental observations accord well with the numerical predictions. Due to their large and tunable mode spacing, robustness, and flexibility, the proposed dual-pumped OFCs could find potential applications in a wide range of fields, including arbitrary optical waveform generation, high-capacity optical communications, and signal-processing systems.

Millimeter-resolution long-range OFDR using ultra-linearly 100 GHz-swept optical source realized by injection-locking technique and cascaded FWM process.

In this paper, we propose and demonstrate a millimeter-resolution long-range optical frequency domain reflectometry (OFDR) using an ultra-linearly 100-GHz swept optical source realized by injection-locking technique and cascaded four-wave-mixing (FWM) process. The ultra-linear sweep is realized using an external modulation method with a linearly swept radio frequency (RF) signal. The RF signal sweeps from 16 GHz to 19.3 GHz, and the slave laser is injection-locked to the 8th-order sideband of the master laser, achieving a frequency sweeping span of ~25 GHz. By using the injection-locked frequency-swept laser as the optical source of OFDR, we obtain a spatial resolution of 4.2 mm over 10-km measurement range. A polarization beat length of 10.5 cm is measured benefiting from the high spatial resolution. To improve the spatial resolution further, FWM process is used to broaden the frequency sweeping span. Frequency sweeping span of ~100 GHz is achieved with cascaded FWM. We demonstrate a 1.1-mm spatial resolution over 2-km measurement range with the proposed ultra-linearly swept optical source.

Enhancement of entanglement using cascaded four-wave mixing processes.

A maximal joint quadrature squeezing of -6.8±0.4 dB is experimentally obtained by a scheme of cascaded four-wave mixing (FWM) processes, which gives strong proof about the inseparability or entanglement between output of the twin beams from the system. Here joint quadrature is the difference between the two quadratures of the twin beam output from the cascaded FWM processes. This result is enhanced by about 3.1 dB, compared with the one of the single FWM process. We also study the gain dependence of the entanglement enhancement in this cascaded system. Theoretical predictions with the considerations of the losses in the experiment are also studied, and a similar trend in the low-gain regime can be found between the experimental results and the theoretical predictions. The scheme of cascaded FWM processes, which can be used to improve or even manipulate the degree of the entanglement between the output fields from the single FWM process, may find its applications in the continuous-variable quantum communication protocols.

Characterization of Pairwise Correlations from Multiple Quantum Correlated Beams Generated from Cascaded Four-Wave Mixing Processes

We theoretically characterize the performance of the pairwise correlations (PCs) from multiple quantum correlated beams based on the cascaded four-wave mixing (FWM) processes. The presence of the PCs with quantum corre- lation in these systems can be verified by calculating the degree of intensity difference squeezing for any pair of all the output fields. The quantum correlation characteristics of all the PCs under different cascaded schemes are also discussed in detail and the repulsion effect between PCs in these cascaded FWM processes is theoretically predicted. Our results open the way for the classification and application of quantum states generated from the cascaded FWM processes.

Phase-sensitive cascaded four-wave-mixing processes for generating three quantum correlated beams

Theoretical studies and experimental implementations of quantum correlation are the important contents of continuous variables quantum optics and quantum information science. There are various systems for the study of quantum correlation. Here, we study an experimental scheme for generating three quantum correlated beams based on phase-sensitive cascaded four-wave-mixing (FWM) processes in rubidium vapor. Quantum correlation including intensity difference or sum squeezing, two other combinatorial squeezing, and quantum entanglement among the three output light fields are theoretically analyzed in this paper. Also, the comparison of the quantum correlations have been made between the phase-sensitive cascaded FWM processes and the phase-insensitive cascaded FWM processes. By changing the phases and intensities of the input beams, it is interesting to find that the maximum degrees of various combinatorial squeezing are equal when the two FWM processes share a common intensity gain. When the common intensity gain of the two FWM processes changes, the maximum degrees of different combinatorial squeezing will be synchronously controlled. At last we discuss the genuine tripartite entanglement and steering in our phase-sensitive cascaded scheme, and compare them with the cases of the phase-insensitive cascaded scheme.

Generation of tripartite entanglement from cascaded four-wave mixing processes.

We investigate the possibility of an experimentally feasible cascaded four-wave mixing (FWM) system [Phys. Rev. Lett. 113, 023602 (2014)] to generate tripartite entanglement. We verify that genuine tripartite entanglement is present in this system by calculating the covariances of three output beams and then considering the violations of the inequalities of the three-mode entanglement criteria, such as two-condition criterion, single-condition criterion, optimal single-condition criterion and the positivity under partial transposition (PPT) criterion. We also consider the possibilities of the bipartite entanglement of any pair of the three output beams using the Duan-Giedke-Cirac-Zoller criterion and PPT criterion. We find that the tripartite entanglement and the bipartite entanglement for the two pairs are present in the whole gain region. The entanglement characteristics under different entanglement criteria are also considered. Our results pave the way for the realization and application of multipartite entanglement based on the cascaded FWM processes.

0.1–1-THz High-Repetition-Rate Femtosecond Pulse Generation From Quasi-CW Dual-Pumped All-Fiber Phase-Locked Kerr Combs

We report the generation of tunable high-repetition-rate (0.1–1 THz) femtosecond pulses based on a quasi-continuous wave (CW) dual-pumped all-fiber cascaded four-wave-mixing (FWM) scheme without requiring a cavity resonator. By synchronously injecting two pulse-modulated lasers into an 85-m-long dispersion-flat highly nonlinear fiber, cascaded FWM processes under only ∼30-mW average pump power are efficiently initiated to form the Kerr frequency combs near 1.56 $\mu\text{m}$ . Phase locking of the Kerr combs is confirmed by real-time measurements using an autocorrelator, and stable ultrashort pulse trains are observed. The pulse repetition rate can be tuned continuously in the range of 0.1∼1 THz by controlling the wavelength spacing between the two pump lasers. The pulse duration can be correspondingly adjusted from 1.66 ps to 262 fs. Such quasi-CW dual-pumped all-fiber cascaded-FWM frequency combs with the advantages of compactness and flexibility could provide a practical solution for generating ultrahigh-repetition-rate femtosecond pulses.

Quantum optical devices based on four-wave mixing in hot rubidium vapor

In this paper, we briefly review the recent experimental progresses in quantum optics based on four-wave mixing (FWM) processes in hot rubidium vapor, particularly our two recent experiments in quantum information. We have experimentally produced strong quantum correlations between three bright beams generated by two cascaded FWM processes. The intensity difference squeezing with the cascaded system is enhanced to (-7.0±0.1)dB from the (-5.5±0.1)dB/(-4.5±0.1)dB with only one FWM process. Also, this system can be easily extended to multiple modes using multiple FWM processes. Besides, we have also successfully realized a cascade all-optical transistor (AOT), which is driven by a very weak light beam about 800 photons in total. The required probe power for achieving a switching efficiency of 50% can be as low as 180 pW, and it can manipulate a light beam with power of 5.0×106 times more, which proves the cascade of the AOT. Both experiments may find wide applications in quantum information and optical communication.

Experimental generation of multiple quantum correlated beams from hot rubidium vapor.

Quantum correlations and entanglement shared among multiple quantum modes are important for both fundamental science and the future development of quantum technologies. This development will also require an efficient quantum interface between multimode quantum light sources and atomic ensembles, which makes it necessary to implement multimode quantum light sources that match the atomic transitions. Here, we report on such a source that provides a method for generating quantum correlated beams that can be extended to a large number of modes by using multiple four-wave mixing (FWM) processes in hot rubidium vapor. Experimentally, we show that two cascaded FWM processes produce strong quantum correlations between three bright beams but not between any two of them. In addition, the intensity-difference squeezing is enhanced with the cascaded system to -7.0±0.1 dB from the -5.5±0.1/-4.5±0.1 dB squeezing obtained with only one FWM process. One of the main advantages of our system is that as the number of quantum modes increases, so does the total degree of quantum correlations. The proposed method is also immune to phase instabilities due to its phase insensitive nature, can easily be extended to multiple modes, and has potential applications in the production of multiple quantum correlated images.

Nonlinear pulse propagation in a quantum dot laser

We investigate the nonlinear propagation of an ultra-short, 150 fs, optical pulse along the waveguide of a quantum dot (QD) laser operating above threshold. We demonstrate that among the various nonlinear processes experienced by the propagating pulse, four-wave mixing (FWM) between the pulse and the two oscillating counter-propagating cw fields of the laser is the dominant one. FWM has two important consequences. One is the creation of a spectral hole located in the vicinity of the cw oscillating frequency. The width of the spectral hole is determined by an effective carrier and gain relaxation time. The second is a modification of the shape of the trailing edge of the pulse. The wave mixing involves first and second order processes which result in a complicated interaction among several fields inside the cavity, some of which are cw while the others are time varying, all propagating in both directions. The nonlinear pulse propagation is analyzed using two complementary theoretical approaches. One is a semi-analytical model which considers only the wave mixing interaction between six field components, three of which propagate in each direction (two cw fields and four time-varying signals). This model predicts the deformation of the tail of the output signal by a secondary idler wave, produced in a cascaded FWM process, which co-propagates with the original injected pulse. The second approach is a finite-difference time-domain simulation, which considers also additional nonlinear effects, such as gain saturation and self-phase modulation. The theoretical results are confirmed by a series of experiments in which the time dependent amplitude and phase of the pulse after propagation are measured using the cross-frequency-resolved optical gating technique.