The squeezed light field in the band of alkali metal atomic transitions is an important quantum resource in the field of quantum information and precision measurement. The wavelengths of atomic transition lines (760–860 nm) are relatively short. Limited by the gray-tracking effect of nonlinear crystals, the squeezing degree of the squeezed light in this band generated by the optical parametric amplifiers is low. Now, the squeezing is about 3–5 dB. Considering the problems in the experimental generation of the squeezed light at the wavelengths of atomic transitions, the variation law of quantum noise of the light field output from the single optical parametric amplifier with its physical parameters is studied theoretically, and the optimal physical parameters are obtained. To further improve the squeezing in the band of alkali metal atomic transitions, the cascaded optical parametric amplifiers are considered. Based on the basic theory of the optical parametric amplifiers, the theoretical model of the cascaded optical parametric amplifiers is constructed, in which the optical loss and phase noise of the cascaded optical loops are considered. Based on this, the quantum noise characteristics of the light field output from the cascaded system versus the optical loss and phase noise are analyzed at the frequencies of 2 MHz and 100 kHz, respectively. It is found that for the squeezing at 2 MHz, cascading 2 to 3 optical parametric amplifiers can significantly improve the squeezing under the premise of the low optical path loss and phase noise; for the squeezing in the low-frequency band, the enhancement of the squeezing for the cascaded system is quite weak. Under the current experimental parameters, the squeezing at 2 MHz of the squeezed light on rubidium resonance can be improved from –5 dB to –7 dB by cascading another DOPA. For the squeezing at low frequency band, the cascaded system proves to be useless, and the efforts should be made to reduce the technique noise in the low frequency band. Furthermore, the quantum limit and spectral characteristics of the squeezed light field output from the cascaded system are further explored. This study can provide reference and guidance for the improvement in the squeezing degree of the band of atomic transitions.
The squeezed light field in the band of alkali metal atomic transitions is an important quantum resource in the field of quantum information and precision measurement. The wavelengths of atomic transition lines (760–860 nm) are relatively short. Limited by the gray-tracking effect of nonlinear crystals, the squeezing degree of the squeezed light in this band generated by the optical parametric amplifiers is low. Now, the squeezing is about 3–5 dB. Considering the problems in the experimental generation of the squeezed light at the wavelengths of atomic transitions, the variation law of quantum noise of the light field output from the single optical parametric amplifier with its physical parameters is studied theoretically, and the optimal physical parameters are obtained. To further improve the squeezing in the band of alkali metal atomic transitions, the cascaded optical parametric amplifiers are considered. Based on the basic theory of the optical parametric amplifiers, the theoretical model of the cascaded optical parametric amplifiers is constructed, in which the optical loss and phase noise of the cascaded optical loops are considered. Based on this, the quantum noise characteristics of the light field output from the cascaded system versus the optical loss and phase noise are analyzed at the frequencies of 2 MHz and 100 kHz, respectively. It is found that for the squeezing at 2 MHz, cascading 2 to 3 optical parametric amplifiers can significantly improve the squeezing under the premise of the low optical path loss and phase noise; for the squeezing in the low-frequency band, the enhancement of the squeezing for the cascaded system is quite weak. Under the current experimental parameters, the squeezing at 2 MHz of the squeezed light on rubidium resonance can be improved from –5 dB to –7 dB by cascading another DOPA. For the squeezing at low frequency band, the cascaded system proves to be useless, and the efforts should be made to reduce the technique noise in the low frequency band. Furthermore, the quantum limit and spectral characteristics of the squeezed light field output from the cascaded system are further explored. This study can provide reference and guidance for the improvement in the squeezing degree of the band of atomic transitions.
The squeezing level of light on atomic resonance produced by a degenerate optical parametric amplifier (DOPA) is now limited by blue or violet pump-light-induced loss, and it is difficult to improve the squeezing by simply reducing the loss of DOPA. In this study, two promising schemes, namely, the cascaded DOPA (C-DOPA) and the coherent feedback-controlled DOPA (CFC-DOPA), are theoretically discussed. For a ideal case, the CFC-DOPA can realize infinite squeezing output but requires almost infinite accuracy in phase locking. For a practical case with feasible physical parameters of realistic systems, the performance of squeezing enhancement for the C-DOPA and CFC-DOPA is compared. The C-DOPA shows advantages in the megahertz frequency range, while the CFC-DOPA shows advantages in the low-frequency range. At a general analysis frequency of 2 MHz, C-DOPA shows better robustness against the loss of the system. As a price, it requires a smaller instability tolerance for phase locking. With the C-DOPA, the squeezing on Rb atomic resonance can be pushed from − 5 d B to − 7 d B . Our analytical results can provide a valuable reference for designing experimental devices to efficiently produce high-quality squeezed light on atomic resonance, which has potential applications in quantum information processing and quantum metrology.
Squeezed states are important sources in quantum physics, which have potential applications in fields such as quantum teleportation, quantum information networks, quantum memory, and quantum metrology and precise measurements. For our interest, the squeezed vacuum will be used in the quantum-enhanced optical atomic magnetometers, filling the vacuum port of the probe beam to improve measurement sensitivity. Based on the sub-threshold optical parametric oscillator (OPO) with PPKTP crystal, the squeezed vacuum at rubidium D1 line of 795 nm is obtained. In our work, we investigate the noise sources in an OPO system. By carefully controlling the classical noise source, the squeezing band extends to the analysis frequency of 2.6 kHz. The flat squeezing trace is 2.8 dB below the shot noise limit. In our work, we focus on the difference between the squeezing results at the analysis frequency of kilohertz regime at two different wavelengths, 1064 nm and 795 nm. The difference mainly comes from the absorption of 795 nm laser and its second harmonic at 397.5 nm in crystal (397.5 nm laser is at the edge of transparent window of PPKTP crystal that has an absorption index much higher than at other wavelength). The absorption induced nonlinear loss and thermal instability greatly affect the squeezing results, which is discussed in our work. Squeezing level at 795 nm is worse than at 1064 nm due to the above-mentioned factors. Noise coupling to the detection system limits the squeezing band. In the audio frequency band, squeezing is easily submerged in roll-up noises and the measured squeezing level is limited. Two factors limit the obtained squeezing:the technical noise induced in the detection and the squeezing degradation by the noise coupling of the control beams. In experiment, we carefully control the classical noise at analytical frequency of kilohertz by means of a vacuum-injected OPO, a counter-propagating cavity locking beam with orthogonal polarization, low noise homodyne detector, stable experimental system and quantum noise locking method for squeezing phase locking. Firstly, to preclude the classical noise from coupling the laser source, we use the vacuum injected OPO. A signal beam helps optimize the parametric gain and is blocked in the squeezing measurement process. In order to maintain the OPO, a counter-propagating beam with orthogonal polarization is used for locking the cavity. Then, a low noise balanced homodyne detector with a common-mode rejection ratio of 45 dB helps improve the audio frequency detection. Finally, the quantum noise locking provides a method to lock the relative phase between the coherent beam and the squeezed vacuum field. With the combination of these technical improvements, a squeezed vacuum of 2.8 dB is obtained at the analysis frequency of 2.6-100 kHz. The obtained squeezing level is mainly limited by the relatively large loss in OPO, which is induced by ultra-violet absorption in PPKTP crystal. The generated squeezed field is used to reduce the polarization noise of probe beam in an optical magnetometer, in order to increase detection sensitivity.
We demonstrate the enhanced quantum noise reduction of the output field from an optical parametric amplifier (OPA) by employing the cascaded optical parametric amplifiers (COPA), in which the output field of one OPA is the input field of the subsequent one. The output field noise formulas of the cascaded degenerate and nondegenerate OPAs (CDOPA and CNOPA) are obtained. The analytical results show that a CDOPA and a CNOPA can generate squeezing beams and entangled beams with a wider bandwidth under a low pump parameter, respectively. The cavity output efficiency and the intracavity loss are the main factors for improving the degrees of squeezing and entanglement. Our work will provide improved schemes for designing COPAs to efficiently produce high-quality squeezed and entangled states, which have potential applications in quantum-information processing.
The intensity-difference squeezed state is an important concept in quantum optics, which is not only of great significance for fundamental research in quantum physics, but also an important quantum resource in the fields of quantum communication, quantum computing, and quantum precision measurement. The optical parametric amplifier based on atomic four-wave mixing is one of the most effective means to achieve intensity-difference squeezed light. However, due to the absorption loss of atomic vapor in the light field, the output squeezing still needs improving. By feeding the non-classical optical field from the optical parametric amplifier back to the input port, the quantum characteristics of its output optical field can be enhanced. However, the intensity-difference squeezing enhancement from a phase-insensitive amplifier is experimentally realized based on coherent feedback control. The intensity-difference squeezing enhancement of the phase-sensitive amplifier has not been discussed. In this work, a two-port coherent feedback-controlled phase-sensitive amplifier is analyzed theoretically. The dependence of the intensity-difference squeezing, respectively, on the feedback intensity, the intensity gain of the optical parametric amplifier, and the losses of the system are investigated. For the ideal case in which the losses of the system are ignored, infinite squeezing can be achieved by adjusting the strength and phase of feedback. Considering the actual atomic absorption losses, squeezing enhancement can also be achieved over a wide range of intensity gains within a certain feedback intensity range. In addition, the squeezing enhancement is quite efficient for the medium intensity gain range. The intensity-difference squeezing enhancement strongly depends on the absorption loss of atomic vapor. The smaller the absorption loss, the more significant the squeezing enhancement effect is. Furthermore, the experimental feasibility of this scheme is also considered in detail. Our research can provide useful references for achieving high-quality non classical light fields in experiment, which may find applications in quantum information processing and quantum precise measurement.
Continuous variable (CV) audio-band frequency squeezed states at the fiber telecommunication wavelength is an important quantum resource for the practical applications based on optical fiber. As is well known, the optical power attenuation and phase diffusion effect of light at 1.3 μm in standard telecommunication fibres are low and small, respectively. The audio-band frequency squeezed light at 1.34 μm can be utilized to realize quantum precision measurement, such as quantum-enhanced sensing in the low-frequency range, laser interferometer for gravitational wave detection. In this paper, CV audio-band frequency vacuum squeezed states at 1.3 μm are experimentally generated by using a type-I degenerate optical parametric oscillator (DOPO) below the threshold. A home-made continuous-wave single-frequency dual-wavelength (671 nm and 1.34 μm) Nd:YVO4/LBO laser is used as a pump source for DOPO based on a type-I quasi-phase-matched periodically poled KTiOPO4 (PPKTP) crystal. Mode cleaners with a finesse of 400 and linewidth of 0.75 MHz are used to filter the noise of lasers at 671 nm and 1.34 μm, respectively. The intensity noises of the two lasers reach a shot noise level for analysis frequencies higher than 1.0 MHz and their phase noises reach shot noise level for analysis frequencies higher than 1.3 MHz, respectively. The low noise single-frequency 671 nm laser is utilized as a pump of the DOPO. The threshold power of the DOPO is 450 mW. In order to detect the audio-band frequency vacuum squeezed states, the power of local oscillator of a homodyne detector system is optimized to 60 μupW. Furthermore, the effect of common mode rejection ratio (CMRR) of detectors is discussed in detecting the audio-band frequency vacuum squeezed states. Improvement of CMRR of detectors is a good way to detect the audio-band frequency vacuum squeezed states effectively. When the phase matching temperature of PPKTP crystal is controlled at 53℃ by using a home-made temperature controller and the pump power is 95 mW, the vacuum squeezed states are generated at analysis frequency ranging from 8-100 kHz. A maximum measured squeeze of 5.0 dB is obtained at analysis frequency of 36 kHz. A 3.0 dB squeezed light is obtained at an audio-band frequency of 8 kHz.
A frequency tunable source of squeezed light has been developed for application to a variety of problems in atomic physics. The basic experimental arrangement consists of a subthreshold optical parametric oscillator (OPO) that is pumped by the frequency-doubled output of a titanium-sapphire laser. Squeezed light with continuous tunability of 2 GHz has been generated with a directly observed nonclassical noise reduction of 5.0 dB relative to the vacuumstate limit in a balanced homodyne detector (5.2 dB when corrected for detector noise). Although our source is potentially broadly tunable over the noncritical phase-matching bandwidth of potassium niobate, current research has concentrated on operation at 852 nm for excitation of the D2 line of atomic cesium. Relative to the usual quantum limit associated with vacuumstate fluctuations, enhanced sensitivity is demonstrated for the detection of Doppler-free resonances in FM saturation spectroscopy, with an improvement of 3.1 dB directly observed and 3.8 dB after correction for detector noise.