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arXiv:1505.03649 · Physical Review B

Resonant single-photon and multiphoton coherent transitions in a detuned regime

Sylvain Bertaina, Mathew Martens, Matthieu Egels, Damien Barakel, I. Chiorescu

Published Jul 10, 2015• 7 citations
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Abstract

We performed quantum manipulations of the multilevel spin system $S=5/2$ of a ${\mathrm{Mn}}^{2+}$ ion, by means of a two-tone pulse drive. The detuning between the excitation and readout radio frequency pulses allows one to select the number of photons involved in a Rabi oscillation as well as increase the frequency of this nutation. Thus detuning can lead to a resonant multiphoton process. Our analytical model for a two-photon process as well as a numerical generalization fit well the experimental findings, with implications for the use of multilevel spin systems as tunable solid state qubits.

DOI
10.1103/physrevb.92.024408

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We performed quantum manipulations of the multilevel spin system S=5/2S=5/2S=5/2 of a Mn2+{\mathrm{Mn}}^{2+}Mn2+ ion, by means of a two-tone pulse drive. The detuning between the excitation and readout radio frequency pulses allows one to select the number of photons involved in a Rabi oscillation as well as increase the frequency of this nutation. Thus detuning can lead to a resonant multiphoton process. Our analytical model for a two-photon process as well as a numerical generalization fit well the experimental findings, with implications for the use of multilevel spin systems as tunable solid state qubits.
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 report on multiphoton Rabi oscillations and controlled tuning of a multilevel system at room temperature (S=5/2S=5/2S=5/2 for Mn2+{}^{2+}2+:MgO) in and out of a quasiharmonic level configuration. The anisotropy is much smaller than the Zeeman splittings, e.g., the six-level scheme shows only a small deviation from an equidistant diagram. This allows us to tune the spin dynamics by compensating for the cubic anisotropy with either a precise static-field orientation or a microwave field intensity. Using the rotating-frame approximation, the experiments are explained very well by both an analytical model and a generalized numerical model. The calculated multiphoton Rabi frequencies are in excellent agreement with the experimental data.
Multiphoton blockade provides an efficient way to achieve entangled photon sources and leads to wide applications in modern quantum technologies. Here, we propose a scheme to realize multiphoton blockade by a multitone drive. Specifically, we demonstrate two-photon and three-photon blockades in a single- mode optical Kerr resonator using a two-tone and a three-tone drive, respectively. In comparison with the single-tone drive, except for the blockade of the (n+1)th(n+1)\mathrm{th}(n+1)th photon excitation due to large detuning, the key mechanism in this scheme is the sequentially resonant excitations of all the mmm-photon states $(m\ensuremath{\le}n)$ by the nnn-tone drive, which lead to the enhancement of photon generation and the demonstration of multiphoton blockade in the weak driving regime. Moreover, the photon distribution within the system can be adjusted on demand by tuning the relative amplitudes of the driving fields for different frequencies. The scheme can be extended to other bosonic systems and be applied to demonstrate other multiphoton physical effects.
Multiphoton blockade provides an efficient way to achieve entangled photon sources and leads to wide applications in modern quantum technologies. Here, we propose a scheme to realize multiphoton blockade by a multi-tone drive. Specifically, we demonstrate two-photon and three-photon blockades in a single-mode optical Kerr resonator using a two-tone and a three-tone drive, respectively. In comparison with the single-tone drive, except for the blockade of the (n+1)(n+1)(n+1)th photon excitation due to large detuning, the key mechanism in this scheme is the sequently resonant excitations of all the mmm-photon states (m≤nm\leq nm≤n) by the nnn-tone drive, which lead to the enhancement of photon generation and the demonstration of multiphoton blockade in the weak driving regime. Moreover, the photon distribution within the system can be adjusted on demand by tuning the relative amplitudes of the driving fields for different frequencies. The scheme can be extended to other bosonic systems and be applied to demonstrate other multiphoton physical effects.
We develop a general theory for multiphoton qubit-resonator interactions enhanced by a qubit drive. The interactions generate qubit-conditional operations in the resonator when the driving is near nnn-photon cross resonance, i.e., when the qubit drive is nnn times the resonator frequency. We pay special attention to the strong driving regime, where the resulting effective interactions are conditioned on the qubit dressed states. Next, we investigate the use of a two-tone drive to engineer an effective nnn-photon Rabi Hamiltonian with widely tunable effective system parameters, which could enable the realization of new regimes that have so far been inaccessible. Then, we discuss applications for the specific case where n=2n=2n=2, which results in qubit-conditional squeezing (QCS). We show that the QCS protocol can be used to generate a superposition of orthogonally squeezed states following a properly chosen qubit measurement. We outline quantum information processing applications for these states, including encoding a qubit in a resonator via the superposition of orthogonally squeezed states. We show how the QCS operation can be used to realize a controlled-squeeze gate and its use in bosonic phase estimation. The QCS protocol can also be utilized to achieve faster unitary operator synthesis on the joint qubit-resonator Hilbert space. Finally, we propose a multiphoton circuit QED implementation based on a transmon qubit coupled to a resonator via an asymmetric SQUID. We provide realistic parameter estimates for the two-photon operation regime that can host the aforementioned two-photon protocols. We use numerical simulations to show that, even in the presence of spurious terms and decoherence, our analytical predictions are robust.
When an atom is strongly coupled to a cavity, the two systems can exchange a single photon through a coherent Rabi oscillation. This process enables precise quantum-state engineering and manipulation of atoms and photons in a cavity, which play a central role in quantum information and measurement. Recently, a new regime of cavity QED was reached experimentally where the strength of the interaction between light and artificial atoms (qubits) becomes comparable to the atomic transition frequency or the resonance frequency of the cavity mode. Here we show that this regime can strongly modify the concept of vacuum Rabi oscillations, enabling multiphoton exchanges between the qubit and the resonator. We find that experimental state-of-the-art circuit-QED systems can undergo two- and three-photon vacuum Rabi oscillations. These anomalous Rabi oscillations can be exploited for the realization of efficient Fock-state sources of light and complex entangled states of qubits.