Optical resonator with steep internal dispersion

When a pump field and probe field simultaneously drive an electronic-state atomic transition, the probe field absorption spectrum can consist of an absorption peak centered near \ensuremath{\Delta}'=0 and amplification peak centered near \ensuremath{\Delta}'=2\ensuremath{\Delta} (\ensuremath{\Delta} and \ensuremath{\Delta}' are the pump and probe field detunings from the atomic transition frequency, respectively). This type of spectrum is seen in the limit \ensuremath{\Vert}\ensuremath{\Delta}\ensuremath{\Vert}\ensuremath{\gg}\ensuremath{\chi}\ensuremath{\gg}\ensuremath{\Gamma}, where \ensuremath{\chi} is the Rabi frequency associated with the pump field and 2\ensuremath{\Gamma} is the homogeneous width associated with the atomic transition. For atoms cooled below the recoil limit of laser cooling, the qualitative nature of the probe absorption spectrum can undergo a dramatic change. Provided that the recoil splitting ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$ is larger than the homogeneous decay rate (as might occur in the case of a forbidden transition), the absorption and amplification features each split into an absorption-amplification doublet. In addition, structure is found in the probe absorption spectrum near \ensuremath{\Delta}'=\ensuremath{\Delta}; this structure consists of two absorption-amplification doublets. Both doublets can be resolved if ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$>\ensuremath{\Gamma}. If ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$, one of the doublets can be resolved provided that ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$>${\mathrm{\ensuremath{\Gamma}}}_{\mathit{A}}$, where ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{A}}$ is some effective atomic ground state width in the problem. The positions, widths, and relative weights of all the components are readily predicted using a dressed-atom theory in which quantization of the center-of-mass momentum is included. An analytical expression for the probe field spectrum is obtained for a simple case in which spontaneous decay to the lower level is neglected. Validity criteria for the results are discussed.

We propose a multifunction phase-shifting manipulator with low noise at a single-photon level,by using a threelevel atomic scheme.This three-level system interacts with a strong pumping field and a weak probe field with a large detuning.Due to this large detuning,two lower states can be coherently prepared prior to the injection of the pump and probe fields.In our configuration,the duration of the pumping field is much longer than that of the probe field. By solving the Heisenberg-Langevin equations of our system under the steady state approximation,we calculate the linear susceptibility of the system and examine the quantum noise properties of the probe field in detail.We show that this scheme,which rests on the process of two-wave mixing with initial atomic coherence,exhibits many interesting properties that neither typical electromagnetically induced transparency (EIT) schemes nor active Raman gain (ARG) schemes possess.Although both EIT-and ARG-based schemes have been widely investigated in atomic medium,the direct generalizations of these schemes to the single/few photon limit prove to be more problematic.The low fidelity due to the significant probe-field attenuation in EIT medium and the large quantum noise due to the amplification of the probe field in an active Raman gain medium are the main obstacles that prohibit a high-fidelity,low-noise phase shifter from being realized in the single/few photon limit.Physically,this scheme can be viewed as a hybrid scheme in which two processes of different physical principles are allowed to interfere with each other to achieve many desired functionalities. For instance,it can be used as a lossless two-photon-broadband phase-shifter with suitable system parameters.It can also be used as an attenuator/amplifier and a total transparency with a zero phase shift.In particular,we show that by locking the pump field intensity and the two-photon detuning simultaneously a flat constant π-phase shift can be realized with unit probe fidelity in a broad probe field frequency range.Applying the quantum regression theorem,we calculate the noise spectrum of the outgoing probe field as a large phase shift is achieved,and show that this two-photon-insensitive π-phase shift may significantly reduce the quantum noise fluctuations associated with a Raman gain process,and have a lot of potential applications for quantum information processing and optical telecommunication.The realization of this broadband π-phase-shift with significantly reduced quantum noise fluctuations makes this scheme attractive for the realization of low-noise phase-gate/polarization-gate at single-photon level.

We study Raman scattering in molecular media by applying two laser fields in a two-photon resonance with vibrational transition. The role of rotational levels has been investigated. It is shown that the molecular vibrational coherence strongly depends on the effect of coherent population trapping for rotational levels. The obtained results are important for application of Raman spectroscopy to molecular detection for engineering, chemical, and biological applications.

We experimentally observe the interference patterns of vortex probe transmission signal (PTS) and vortex four-wave mixing (FWM). By changing the difference in the divergences of two optical beams, the spiral interference patterns of the probe beam and the reference Gaussian probe beam can be obtained. It is found that in the interference patterns of vortex PTS, the shifting of the fork can be regulated by blocking different dressing fields and tuning the probe frequency. When the two-photon resonance condition is satisfied, the shift of the fork is the weakest since the strongest probe field intensity induces the weak nonlinear phase shift. In addition, we realize that the relationship between the intensities of the vortex FWM signal and the probe field is not monotonic, because both the intensity of probe field and the dressing effect will affect the intensity of the vortex FWM signal. We also find that the spatial modulations including shifting and splitting are also regulated by the intensity of the probe field and the coupling field. Here, the explanation of these phenomena is presented by the transition of the nonlinear refraction index. Finally, we realize that the singularity overlap or separation between the linear probe and the third-order vortex FWM will lead to the change of fork quantity. Our research is helpful to understand and manipulate optical vortices and can be widely used in quantum computation and communication.

Cavity linewidth engineering from tunneling induced transparency to Autler–Towns splitting

We study the directional amplification of an optical probe field in a three-mode optomechanical system, where the mechanical resonator interacts with two linearly-coupled optical cavities and the cavities are driven by strong optical pump fields. The optical probe field is injected into one of the cavity modes, and at the same time, the mechanical resonator is subject to a mechanical drive with the driving frequency equal to the frequency difference between the optical probe and pump fields. We show that the transmission of the probe field can be amplified in one direction and de-amplified in the opposite direction. This directional amplification or de-amplification results from the constructive or destruction interference between different transmission paths in this three-mode optomechanical system.

We theoretically investigate the tunable delay and advancement of microwave signals based on bichromatic electromechanically induced transparency in a three-mode circuit electromechanical system, where two nanomechanical resonators with closely spaced frequencies are independently coupled to a common microwave cavity. In the presence of a strong microwave pump field, we obtain two transparency windows accompanied by steep phase dispersion in the transmitted microwave probe field. The width of the transparency window and the group delay of the probe field can be controlled effectively by the power of the pump field. It is shown that the maximum group delay of 0.12 ms and the advancement of 0.27 ms can be obtained in the current experiments.

To achieve high degree of quantum noise squeezing, an optical cavity is often employed to enhance the interaction time between light and matter. Here, we propose to utilize the effect of coherent population trapping (CPT) to directly generate squeezed light without any optical cavity. Combined with the slow propagation speed of light in a CPT medium, a coherent state passing through an atomic ensemble with a high optical density (OD) can evolve into a highly squeezed state even in a single passage. Our study reveals that noise squeezing of more than $10$ dB can be achieved with an OD of 1,000, which is currently available in experiments. A larger OD can further increase the degree of squeezing. As the light intensity and two-photon detuning are key factors in the CPT interaction, we also demonstrate that the minimum variance at a given OD can be reached for a wide range of these two factors, showing the proposed scheme is flexible and robust. Furthermore, there is no need to consider the phase-matching condition in the CPT scheme. Our introduction of high OD in atomic media not only brings a long light-matter interaction time comparable to optical cavities, but also opens new avenue in the generation of squeezed light for quantum interface.

The interactions of a three-level atomic system with a single mode of quantized field is investigated analytically. The effect of coherent population trapping is demonstrated for an arbitrary initial quantum field state and the peculiarities of this regime in squeezed vacuum light are found. Mutual influence between atomic and field subsystems and their entanglement arising during the interaction is demonstrated. A significant change of the field state during the interaction is shown. The possibility of photon bunching and anti-bunching and the formation of a quantum field with non-Gaussian properties is found.

The article presents the results of the development, fabrication and investigation of miniature cesium vapor cells for quantum frequency standards with optical pumping, working on the effect of coherent population trapping. Microelectromechanical systems technologies were used in the manufacture of cells. For the first time, the dry silicon etching in inductively coupled plasma of sulfur hexafluoride and freon gas in a mixed mode was used to form internal cavities of cells with a thickness of 1.5 mm. Vacuum-tight sealing of cells containing a solid-state source of cesium vapor and buffer gas was carried out by anodic bonding of glass and silicon in a neon atmosphere. The coherent population trapping signal with a linewidth of 750 Hz and a signal-to-noise ratio of 1190 in the 1-Hz bandwidth was observed. Experimental results show that these microcells are appropriate for applications to atomic clock with a relative frequency stability of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$6\cdot 10^{-11}$</tex> at 1 s.

We examine experimentally and theoretically the Ramsey effects on the coherent population trapping (CPT) resonance in a paraffin-coated Rb vapor cell. The observed CPT spectrum in the Hanle configuration of the 5S1/2(F = 2)−5P1/2(F′ = 1) transition of 87Rb atoms consists of a narrow structure with a spectral width of 0.10 mG due to the wall-induced Ramsey effect and a broad structure with a spectral width of 23 mG due to the transit effect. Considering the velocity distribution of atoms and the number of wall-atom collisions, we numerically calculated the transmittance of the laser beam as a function of the longitudinal magnetic field. The experimental results of the CPT Ramsey interference were in good agreement with the theoretical results, and the dependences of the CPT Ramsey effects on the atom-laser interaction time were investigated in detail.

A three-level lambda system driven by multicolor control, pump, and probe fields is investigated. The pump and probe fields are derived from the same laser with opposite propagating directions. Due to the Doppler effect, the zero group-velocity atoms face bichromatic fields, while other atoms face trichromatic fields. The atomic medium shows distinct characteristics and exhibits simultaneous electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) at two frequencies. EIT and EIA peaks have a fixed relationship with frequency, which is determined by the Doppler shifts.

Motivated by a recent experiment, the author presents a theoretical study on optical absorption in a semiconductor subjected to pump and probe radiation fields. The electron and hole interactions with midinfrared pump and probe fields are considered and the absorption coefficient is calculated on the basis of a Boltzmann equation approach. It is found that the results obtained theoretically are in line with those observed experimentally and can be used to understand important experimental findings such as the optical absorption in the forbidden zone and the dependence of the absorption of the probe field on intensity and frequency of the pump field.

We present a convenient and efficient scheme to generate arbitrarily multipartite continuous-variable entanglement via mechanical oscillator displacement induced by two strong input pump fields in the conventional single-cavity optomechanical system. It is shown that multipartite entanglement among the outputs of the two pump fields and any number of relatively weak probe fields can be realized and optimized when the two pump fields with suitable amplitude ratio and relative initial phase are, respectively, tuned to the red and blue mechanical sidebands of a single cavity mode and each probe field is red-detuned by the mechanical frequency with respect to a different neighboring cavity mode. This method can, in principle, be extended to flexibly and conveniently generate arbitrarily multiple nondegenerate bright entangled fields by using only coherent laser fields, and may find promising applications in realistic quantum communication and networks.

Tunable high-order sideband generation has important applications in the realization of the optical frequency comb with a varying spectral region (corresponding to the sideband range) and frequency resolution (corresponding to the sideband interval). In this paper, we propose a theoretical scheme to tune both the range and the interval of the high-order sidebands in a coupled double-cavity optomechanical system, which consists of an optomechanical cavity and an auxiliary cavity. Our proposal can be realized by driving the optomechanical cavity with a control field and a probe field simultaneously, driving the auxiliary cavity with a pump field. Furthermore, we assume that the frequency detuning between the control field and the probe field (the pump field) equals ωb/n (ωb/m), where ωb is the mechanical frequency, m and n are integers. When n = m = 1, we find that the sideband range can be effectively enlarged by increasing the pump amplitude or the photon-hopping coupling rate, or by decreasing the auxiliary cavity damping rate. When n = 1 and m > 1, the output spectrum consists of a series of integer-order sidebands, fraction-order sidebands, and the sum and difference sidebands, and the sideband interval becomes ωb/m and can be diminished by simultaneously increasing m and the pump amplitude.