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Results in Physics

Hook-and-Loop laser fastening of an optical frequency comb to a strongly driven two-level quantum system

Gilbert Reinisch

Published Jan 6, 2022• 1 citation
Publisher

Abstract

In order to control the state of a two-level quantum system (e.g. the spin state of an ion qubit), optical frequency combs perform a two-photon stimulated Raman process through stimulated absorption from one comb tooth and stimulated emission into another comb tooth. If the two-level energy gap is an integer multiple of the repetition rate of the laser, resonant Rabi oscillations are excited. When these latter have a frequency close to the qubit’s transition one, a strongly anharmonic phase-locked cycle may exist on the Bloch sphere, which generates a sub-harmonic series of very narrow, equally spaced, spectral lines. If the repetition rate of an optical frequency comb is appropriately tuned to these latter (up to the average carrier envelope frequency), a highly resonant dynamical regime of the two-level system should be reached where the Raman stimulated absorption and emission processes would occur for any pair of adjacent comb teeth.

DOI
10.1016/j.rinp.2021.105136

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In order to control the state of a two-level quantum system (e.g. the spin state of an ion qubit), optical frequency combs perform a two-photon stimulated Raman process through stimulated absorption from one comb tooth and stimulated emission into another comb tooth. If the two-level energy gap is an integer multiple of the repetition rate of the laser, resonant Rabi oscillations are excited. When these latter have a frequency close to the qubit’s transition one, a strongly anharmonic phase-locked cycle may exist on the Bloch sphere, which generates a sub-harmonic series of very narrow, equally spaced, spectral lines. If the repetition rate of an optical frequency comb is appropriately tuned to these latter (up to the average carrier envelope frequency), a highly resonant dynamical regime of the two-level system should be reached where the Raman stimulated absorption and emission processes would occur for any pair of adjacent comb teeth.
We investigate how the quantum control of a two-level system (TLS) coupled to photons can modify and tune the TLS's photon absorption spectrum. Tuning and controlling the emission and the absorption are of great interest, e.g., for the development of efficient interfaces between stationary and flying qubits in modern architectures for quantum computation and quantum communication. We consider periodic pulse control, where the TLS is subjected to a periodic sequence of the near-resonant Rabi driving pulses, each pulse implementing a ${180}^{\ensuremath{\circ}}$ rotation. For small interpulse delays, the absorption spectrum features a pronounced peak of stimulated emission at the pulse frequency, similar satellite peaks with smaller spectral weights, and the net absorption peaks on the sides. As long as the detuning between the carrier frequency of the driving and the TLS transition frequency remains moderate, this spectral shape shows little change. Therefore, the pulse control allows shifting the absorption peak to a desired position and locks the overall absorption spectrum to the carrier frequency of the driving pulses. A detailed description of the spectrum and its evolution as a function time, the interpulse spacing, and the detuning is presented.
Summary form only given. Here, we demonstrate the first scheme to generate pulsed quantum frequency combs without the need for an external laser. We constructed a laser cavity (Fig. 1a) around a 4-port integrated micro-ring resonator, featuring narrow bandpass filters to select a single resonance, an optical gain component (erbium-doped fiber amplifier), and a mode-locking element (an intensity modulator). By setting the intensity modulation frequency to the fundamental repetition rate of the cavity (determined by the external cavity length), we achieved mode-locked pulsed operation (Fig. 1b), exciting a pulsed two-photon comb. Driving the intensity modulator at multiples of the fundamental repetition rate (upwards of 4x) also resulted in stable mode-locking (Fig. 1c), significant as this enables an increase of the photon pair generation rate without sacrificing its coincidence-to-accidental ratio (CAR). We characterized the photon statistics as a function of the average ring input power (see Fig. 1d), achieving a maximum CAR of 110 that decreases with increasing power and increasing coincidence rates. Autocorrelation measurements confirmed the purity of the generated state (pure single-frequency modes, even at multiples of the repetition rate), confirming that the resonance was excited over its entire bandwidth, and obtained a heralded anti-bunching dip of 0.245<;0.5 as expected of a source operating in the single-photon regime.
We demonstrate the generation of multiphoton quantum states of light by cavity-enhanced parametric down-conversion in the high-repetition-rate pulsed regime. An external enhancement cavity resonant with the spectral comb of modes of a mode-locked pump laser provides a coherent buildup of the pump intensity and greatly enhances the parametric gain without sacrificing its high repetition rate and comb structure. We probe the parametric gain enhancement by the conditional generation and tomographic analysis of two-photon Fock states. Besides its potential impact for efficiently generating highly nonclassical or entangled multiphoton states in many existing experimental setups, this scheme opens exciting perspectives toward the combination of quantum and comb technologies for enhanced measurements and advanced quantum computation protocols.
In the framework of the nonsecular perturbation theory based on the Bogoliubov averaging method, the coherent dynamics of multiphoton Raman transitions in a two-level spin system driven by an amplitude-modulated microwave field is studied. Closed-form expressions for the Rabi frequencies of these transitions are obtained beyond the rotating-wave approximation for the low-frequency driving component. It is shown that spin states dressed by the high-frequency component of the driving field are shifted due to the Bloch-Siegert-like effect caused by antiresonant interactions with the strong low-frequency driving. We predict that with increasing the order of the Raman transition, the Rabi frequency decreases and the contribution of the Bloch-Siegert shift to this frequency becomes dominant. It is found that the amplitude and phase of the Rabi oscillations strongly depend on the initial phase of the low-frequency field as well as on detuning from multiphoton resonance. The recent experimental data for the second- and third-order Raman transitions observed for the nitrogen-vacancy center in diamond (Z. Shu et al., arXiv:1804.10492) are well described in the frame of our approach. Our results may provide new possibilities for coherent control of quantum systems.
We have calculated the excitation spectra of a single electron in the excited state of a three-level atom interacting with two off-resonant laser fields at high intensities. We have also considered the process where one laser photon is absorbed by the ground state, as well as a Raman-type process where one photon of one of the laser fields is emitted while another photon of the other laser field is absorbed simultaneously by the second excited state of the atom. The net excitation spectra of the three processes in question consist of two peaks having always positive intensities indicating induced absorption (attenuation) and a third peak which has positive, zero and negative intensities for values of the Rabi frequencies , and , respectively. When , the Raman-type process prevails over the other two, and the resulting peak has a negative intensity indicating that significant amplification is likely to occur at the corresponding frequency.
Stimulated Raman transition is a fundamental method to coherently manipulate quantum states in different physical systems. Phase-coherent dichromatic radiation fields matching the energy level splitting are the key to realizing stimulated Raman transition. Here we demonstrate a flexible-tuning, spectrum-clean and fiber-compatible method to generate a highly phase-coherent and high-power multi-tone laser. This method features the utilization of a broadband fiber Mach–Zehnder modulator working at carrier suppression condition and second harmonic generation. We generate a multi-tone continuous-wave 532 nm laser with a power of 1.5 Watts and utilize it to manipulate the spin and motional states of a trapped 171Yb+ ion via stimulated Raman transition. For spin state manipulation, we acquire an effective Rabi frequency of 2π × 662.3 kHz. Due to the broad bandwidth of the fiber modulator and nonlinear crystal, the frequency gap between tones can be flexibly tuned. Benefiting from the features above, this method can manipulate 171Yb+ and 137Ba+ simultaneously in the multi-species ion trap and has potential to be widely applied in atomic, molecular and optical physics.