Eight-wave Mixing Research Articles

Three types of third-order non-Hermitian interaction of spontaneous six-wave and eight-wave mixing under multi-dressing effects

Non-Hermitian degeneracy, also known as exceptional point, has been recently seen as a new way to engineer the response of open physical systems. Based on natural non-Hermitian atomic coherence, we investigate spontaneous six-wave mixing (SSWM) and eight-wave mixing (SEWM) processes under both parity–time (PT) and anti-parity–time (anti-PT) symmetry, and we obtain high-dimensional coherent channels under third-order energy-level splitting. Finally, we reveal that the third-order non-Hermitian interaction between two dressing fields of the nested scheme is the strongest, and the parallel scheme is the weakest, with the cascade scheme considered intermediate between them. It can also be used to develop quantum memory devices with enhanced sensitivity in the atom-like system.

Eight Wave Mixing Process is suitable to make Single Photon Source for Quantum Cryptography

Single photon source for use in quantum cryptography should show higher order photon antibunching. We have analyzed non classical effect i.e. higher order photon antibunching in pump mode of eight-wave mixing non linear optical process using short time interaction technique and also the dependence of non classicality on the number of photons prior to interaction in non linear medium. Further we have reported that higher the order of photon antibunching, higher will be the probability to generate single photon source utilized in quantum cryptography.

Field-resolved high-order sub-cycle nonlinearities in a terahertz semiconductor laser

The exploitation of ultrafast electron dynamics in quantum cascade lasers (QCLs) holds enormous potential for intense, compact mode-locked terahertz (THz) sources, squeezed THz light, frequency mixers, and comb-based metrology systems. Yet the important sub-cycle dynamics have been notoriously difficult to access in operational THz QCLs. Here, we employ high-field THz pulses to perform the first ultrafast two-dimensional spectroscopy of a free-running THz QCL. Strong incoherent and coherent nonlinearities up to eight-wave mixing are detected below and above the laser threshold. These data not only reveal extremely short gain recovery times of 2 ps at the laser threshold, they also reflect the nonlinear polarization dynamics of the QCL laser transition for the first time, where we quantify the corresponding dephasing times between 0.9 and 1.5 ps with increasing bias currents. A density-matrix approach reproducing the emergence of all nonlinearities and their ultrafast evolution, simultaneously, allows us to map the coherently induced trajectory of the Bloch vector. The observed high-order multi-wave mixing nonlinearities benefit from resonant enhancement in the absence of absorption losses and bear potential for a number of future applications, ranging from efficient intracavity frequency conversion, mode proliferation to passive mode locking.

Generation of multimode quantum correlation with energy-level cascaded four-wave mixing processes

Multimode quantum correlation has important applications in the field of quantum information. In this paper, we propose a compact scheme to generate multiple quantum correlated beams based on energy-level cascaded four-wave mixing (EC-FWM) process in a single atomic medium of rubidium. Injecting two strong pump beams with different frequencies and one weak probe beam into one rubidium vapor, four possible parametrically amplified FWM (PA FWM) processes can coexist under different phase matching conditions. Within the scheme, the weak probe beam is amplified and three coherent beams are generated, which can also be seen as an eight-wave mixing (EWM) process when certain phase matching condition is satisfied. Based on the energy level system of the scheme, three different cascaded structure models are employed to study the quantum correlation between the four generated beams. Amplitude and phase quadratures squeezing and intensity squeezing of the three- and four-mode are calculated via the input–output relations of the system. We found versatile multimode squeezing can be generated in all the structures, but the degree of squeezing and its distribution among the modes are different, depending on the specific structure. Furthermore, the relation of the quantum correlation, as well as the eigenmodes and eigenvalues of the four-mode quantum states are studied.

Experimental Implementation of a Raman-Assisted Eight-Wave Mixing Process

Engineering higher-order nonlinear interactions is vital in autonomous protection of quantum systems against errors. Such interactions are often not directly available, though, or are slow compared to error rates of the system. The authors present a nonlinear eight-wave mixing process that exchanges four photons of a harmonic oscillator with two excitations of a transmon-qubit mode and two pump photons, by combining more accessible lower-order interactions via a sort of Raman transition. Surprisingly, this technique produces a stronger interaction than a six-wave mixing process in the same system. This eight-wave mixing process is expected to become a key component of autonomous continuous-variable quantum error correction.

Double-dressing tri and quad-photon correlations in spontaneous six and eight-wave mixing

The generation of a nonclassical multi-photon has aroused renewed interest in recent years. Here, we propose a new method to generate tri-photon and quad-photon correlations in time via a double-dressing spontaneous six-wave mixing and eight-wave mixing process in an atomic ensemble, respectively. When we only consider the nonlinear optical response, the coincidence counts of tri and quad photon serves as damped coherent Rabi oscillation. The coincident count of tri (quad) photon contains three (four) conditional two-photon correlation with 10 or 30 (26, 28 or 38) periods, corresponding to 11 or 19 (18 or 20) modes. These mode and periods of tri and quad photon result from destructive interference from the possible 4 or 8 six wave and 18 eight wave coherent channels, respectively. In addition, for tri-photon, the greater double-dressing field strength is, the fewer the number of periods are. The coherent times are also controlled by the double-dressing effect. Such results have potential applications in multi-mode quantum communication and quantum network.

Novel Rydberg eight-wave mixing process controlled in the nonlinear phase of a circularly polarized field.

Eight-wave mixing (EWM) is a seven-order nonlinear process that can reflect nonclassical features within multiple optical fields, thus imparting certain advantages. In this study, we directly observed the EWM spectrum and spatial images that show Rydberg atoms under a circularly polarized probe field in a five-level coherently prepared atomic system. Such circular polarization dressing fields can obtain high-contrast Rydberg EWM overcome the difficulties of several multi-wave mixing (MWM) signals always coexist, and the multi-parameter controlling Rydberg EWM mechanism is established by changing the power and detuning and polarization of the dressing fields. These controllable high-order MWM processes present a contrast ratio of 96% and a narrow linewidth of <30 MHz compared with low-order mixing processes under identical conditions (e.g., six-wave mixing). The corresponding MWM spatial images are presented, and they can partly reflect the underlying nonlinear phase variation, whereas the given theory can predict the experimental results.

Eight-wave mixing parametrical amplification.

We investigate parametrically amplified eight-wave mixing (PA-EWM). The double dressed PA-four-wave mixing (PA-FWM) is the superposition of one PA-FWM process, two different PA-six-wave mixing (PA-SWM) processes (PA-SWM1 and PA-SWM2 with external dressing field 776nm and 795nm, respectively) and one PA-EWM process. When the phases among FWM, SWM1, SWM2 and EWM change from 0 to π, the double dressed PA-FWM could gradually satisfy the pure enhancement (all 0), partial enhancement and suppression (mixture of 0 and π), or pure suppression condition (all π). The outcomes of the investigation can potentially contribute to the development of multi-channel quantum information processing and high dimensional stereoscopic imaging.

Eight-wave mixing process in a Rydberg-dressing atomic ensemble.

We investigate the eight-wave mixing (EWM) process involving highly excited Rydberg states with the assistance of coexisting electromagnetically induced transparency (EIT) windows in a thermal 85Rb vapor both theoretically and experimentally. By use of a disturbance-free optical detection method, the Rydberg EWM characterized by multiple sets of spin coherence is presented via the interplay and competition between the dressing-state effects and excitation blockade caused by strong Rydberg-Rydberg interaction. Such interplay and competition can be demonstrated by the intensity evolutions of multi-wave mixing (MWM) signals via controlling the atomic density, the frequency detuning and Rabi frequencies of corresponding laser fields. The observed Rydberg EWM tailored by EIT windows can possess of much narrower linewidth <30MHz and provide a new way for the study of Rydberg effect in the atomic ensemble above room temperature.

Rydberg six-wave mixing process

We experimentally and theoretically investigate the Rydberg six-wave mixing (SWM) process in 85Rb atomic vapor. Through comparing the center frequency positions of resonant Rydberg SWM signals with different atomic densities, atomic levels induced by van der Waals interaction are observed. Meanwhile, such SWM process which is sensitive to blockade can be modulated by the self-dressing effect and/or external dressing effect. In addition, the Rydberg eight-wave mixing process can be obtained if the power of the external dressing field is low. Such blockaded multi-wave mixing process has potential applications in multi-channel quantum information.

All-solid-state Nd:YAG lasers with self-pumped multiwave-mixing phase conjugate cavities

Several configurations of the laser self-pumped phase-conjugate cavities with multiwave mixing directly in the laser medium based on a single Nd:YAG laser element pumped by multikilowatt laser diode 2D stacks are experimentally studied and compared. In the laser configurations with six- and eight-wave mixing there are generated a high-intensive self-Q-switched 200-ns laser pulse followed by low-intensive free-running lasing. An increase of the number of waves taking part in multiwave mixing from six to eight leads to increase in the laser maximum output energy and optical-to-optical efficiency from 0.55 up to 1.1 J and from 8.3 up to 18% respectively. In the laser configuration with ten-wave mixing the energy characteristic is similar to the same in the laser configuration with eight-wave mixing, but the temporal and spectral characteristics are different from the same in the laser configurations with six- and eight-wave mixing. In last laser configuration not only the first pulse, but also all the train of pulses is generated in high-intensive TEM00 diffraction-limited (M 2 = 1.3---1.5) single-frequency self-Q-switched mode via writing and erasing the gain gratings by the intracavity radiation.

Controlling the transition of bright and dark states via scanning dressing field

We report the transitions between the bright and dark states of singly-dressed four-wave mixing (FWM) and doubly-dressed FWMs, and the corresponding probe transmissions by scanning the dressing field frequency detuning in a five-level atomic system. Moreover, doubly-dressed six-wave mixing with avoided-crossing plots and triple-dressed eight-wave mixing with the comparison of scanning probe field and dressing field are studied. Such controlled transitions of the nonlinear optical signals can be realizable not only in atomic vapors but also in solid medium. The investigations maybe have potential applications in optical communication, quantum information processing and optoelectronic devices, and maybe also provide a sensitive probe method to study the dressing effect.

Normal and higher order squeezing in eight-wave mixing process

We investigate theoretically the generation of squeezed states in spontaneous and stimulated eight wave mixing process. It has been found that squeezing occurs in field amplitude, amplitude-squared, amplitude-cubed and fourth power of amplitude states of fundamental mode in the eight wave mixing process. It is found to be dependent on coupling parameter g interaction time t and phase values of the field amplitude. Eight-wave mixing is a process which involves absorption of three pump photons and emission of four probe photons of same frequency and a signal photon of different frequency. It is shown that squeezing is greater in a stimulated interaction than the corresponding squeezing in spontaneous process. It is found that the degree of squeezing depends upon the photon number in first and higher orders. We study the Poissonian behaviour of quantum field in the fundamental mode. It has been found that the field shows sub-Poissonian behaviour in the fundamental mode. The signal to noise ratio has also been studied in different orders and found to be higher in lower orders.

Polarization interference of multi-wave mixing in a confined five-level system

We investigated the coexisting four-wave mixing, six-wave mixing and eight-wave mixing in ultra-thin, micrometer and long cells. Such multi-wave mixing (MWM) processes can be modified by the polarization interference. The degree of destructive interference of atomic polarizations can be controlled by the wave vector, dressing field and cell length. Specifically, the oscillation behavior of intensity and linewidth of MWM signal results from the destructive interference in ultra-thin cell. For a doubly-dressed four-wave mixing, the inner dressing field suppresses the destructive polarization interference in micrometer and long cells, induces resonance enhancement. However, the outer dressing field only enhances destructive interference.

Controlled multi-wave mixing via interacting dark states in a five-level system

We theoretically investigate the controlled multi-wave mixing (MWM) via interacting multi-dark states in a five-level system. Four-wave mixing (FWM) with three kinds of dual-dressed schemes (nested, sequential, and parallel schemes), six-wave mixing (SWM) with the quadruply nested dressed, and eight-wave mixing (EWM) with the parallel combination of two nested dressed schemes coexisting synchronously in a multi-dressed electromagnetically induced transparency system were well described. Through investigating their spectra, we found that these multi-dressed-states induced by various dressed schemes show strong interaction and interchange. Investigations of these multi-dressing schemes and interactions are very useful for understanding and controlling the generated high-order nonlinear optical signals.

Co-existence of multi-wave mixing in an opening five-level atomic system

We study the co-existence of multi-wave mixing processes in an open five-level atomic system affected by strong coupling fields. Competition among four-wave mixing （FWM） with two dressing fields, the six-wave mixing （SWM） with one dressing field as well as the eight-wave mixing （EWM） propagating along the same direction can be evoked by adjusting laser beams because these multi-wave mixing signals are induced by atomic coherence between common levels. With the dressing fields properly controlled, the FWM and SWM signals can be suppressed while the EWM signals enhanced in the beam. We also amply analyze the difference between the parallel-cascade and sequentical-cascade doubly dressing mechanisms in doubly-dressed four-wave mixing （DDFWM） processes.

Coexistence of four-wave, six-wave and eight-wave mixing processes in multi-dressed atomic systems

Two doubly dressing (parallel and nested processes) schemes are considered which generate co-existing four-wave mixing (FWM), six-wave mixing (SWM) and eight-wave mixing (EWM) processes in an open five-level atomic system. The coherent interaction between two dressing processes in nested type is much stronger than that in parallel type. The singly enhanced SWM and dually enhanced FWM channels can be opened at the same time. Such dramatic enhancements in high-order nonlinear optical processes result from the constructive interactions of double dark resonances. The giant third-, fifth- and seventh-order nonlinear responses with different signs can be obtained by using the coherent phase controls of the polarization beats between the FWM, SWM and EWM signals.

Competition between Dispersion and Absorption of Doubly-Dressed Four-Wave Mixing and Dressed Six-Wave Mixing

We study the competition between dispersion and absorption of doubly-dressed four-wave mixing (DDFWM) and dressed six-wave mixing. In the case of weak coupling fields limit, we find DDFWM signal is affected by destructive interference between four-wave mixing(FWM) and six-wave mixing as well as constructive interference between FWM and eight-wave mixing. By analysing the difference between two kinds of doubly dressing mechanisms (parallel cascade and nested cascade) in this opening five-level system, we can further understand the generated high-order nonlinear optical signal dressed by multi-fields.

Squeezing up to fourth-order in the pump mode of eight-wave mixing process

Squeezing of the electromagnetic field is investigated in the pump mode during an eight-wave mixing process under short time approximation on the basis of quantum mechanical approach. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operator are established. Occurrence of squeezing in the first, second, third and fourth-order field amplitude in the pump mode has been investigated. It depends upon the coupling constant ‘g’ and the phase values of the field amplitude. The process involves absorption of three pump photons of the same frequency, one pump photon of a different frequency and emission of four probe photons of the same frequency. The dependence of squeezing on photon number is established with investigations into the degree of squeezing in the first and higher order. The photon statistics of the pump mode in the process has also been investigated and found to be sub-Poissonian in nature.

Squeezing and photon statistical effects in spontaneous and stimulated eight-wave mixing process

Eight-wave mixing is a process which involves absorption of four pump photons and emission of three probe photons of same frequency and a signal photon of different frequency. Squeezing is investigated in the fundamental mode in spontaneous and stimulated eight-wave mixing process using quantum mechanical approach. The presence of squeezing in field amplitude, amplitude-squared and amplitude-cubed in the fundamental mode has been probed. The dependence of squeezing on photon number is established with investigations into degree of squeezing in the first and higher order of field amplitude. The photon statistics of the field in the fundamental mode has also been investigated. It has been found that the field shows sub-Poissonian behaviour in the fundamental mode.