Effect of the Bloch-Siegert shift on the frequency responses of Rabi oscillations in the case of nutation resonance

Abstract

Resonant interaction between coherent radiation and quantum systems is most often described within the framework of the rotating-wave approximation. In this case, only one of two counter-rotating linearly polarized components of the electromagnetic field interacts efficiently with the quantum system, while the effect of the second component is negligible. When the electromagnetic field is strong, the counter-rotating (the socalled antiresonance) component becomes efficient and the rotating-wave approximation can no longer be used. Violation of the rotating-wave approximation results in the Bloch-Siegert effect [1]. This effect leading to a shift of the resonance frequency is negligible for optical transitions, but becomes significant for precision nuclear magnetic resonance (NMR) experiments [2]. The Bloch-Siegert effect can also give rise to variations important for the operation of quantum computers [3]. At the same time, because of the interference of the counter-rotating electromagnetic-field components, the Bloch-Siegert effect provides a wonderful opportunity to measure not only the amplitude, but also the absolute phase of a monochromatic electromagnetic field [4].Interest has grown recently in studies of the interaction of two-level quantum systems with both continuous-wave [5,6] and pulsed [7] bichromatic radiation formed by fields with strongly different frequencies.Such an interest is explained by the importance and generality of the results for a wide range of physical objects, including, in particular, nuclear and electron spins in the NMR and EPR, double-well quantum dots, flux and charge qubits in superconducting systems, etc. Such systems are described with the use of the dressedstate approach by which the phenomenon of Rabi oscillations is analyzed. Note that the frequency of these oscillations depends on the efficiency of the interaction between the bichromatic radiation and quantum system, while their damping, on the coherence time of the quantum states. When quantum states dressed by the electromagnetic field are studied, the rotating-wave approximation is inevitably violated if the amplitude of the electromagnetic field exciting the transitions between the dressed states is comparable with the dressing-field amplitude. Hereafter, we consider electron two-level spin systems dressed by the bichromatic field formed by transverse microwave (MW) and longitudinal radio-frequency (RF) fields. It is known [7] that dressing by the electromagnetic field converts a twolevel system into a dynamic multilevel system. Since the MW-and RF-field frequencies are drastically different, bichromatic radiation ensures the excitation of intense multiphoton transitions in the case of the EPR. The direct study of the dynamics of multiphoton transi-The dynamics of a two-level spin system dressed by bichromatic radiation is studied under the conditions of double resonance when the frequency of one (microwave) field is equal to the Larmor frequency of the spin system and the frequency of the other (radio-frequency) fiel...

Relaxation, decoherence, and steady-state population inversion in qubits doubly dressed by microwave and radiofrequency fields

“…In such a case the density matrix is The predicted frequencies of the Rabi oscillations between the doubly dressed states were confirmed experimentally [10,12,19] including the Bloch-Siegert effect [11,18,35]. The amplitude of the Rabi oscillations at each frequency is strongly dependent on the RF field phase.…”

“…The multiphoton transitions between the doubly dressed states in the coupled "qubit-bichromatic field" system have been observed in spectral and time-resolved experiments. Doubly dressed states of qubits have been studied in a wide range of physical objects, including, among others, electron and nuclear spins [10,11,13], quantum dots [14,15], superconducting qubits [16], and cold atoms [17]. The splitting of each peak of the initial Mollow triplet into three new ones has been demonstrated at the continuous-wave optical bichromatic excitation of two-level atoms [9].…”

Optical and microwave control of resonance fluorescence and squeezing spectra in a polar molecule

“…Furthermore, the presence of PDMs considerably influences the optical response of a system [38][39][40] leading, for example, to changes in multiphoton resonant excitation [41][42][43], modifications of the saturation of absorption and dispersion [44], creation of second-harmonic generation [45] and correlated photon pairs [46], as well as the opening of new optical transitions [47][48][49]. The bichromatic excitation of quantum systems with PDMs has been studied in a wide range of quantum systems, including electron and nuclear spins [50,51], QDs [52,53], and superconducting qubits [54]. The RFS of an asymmetric QD has been recently analyzed in the regime of dissipative dynamics and weak frequency modulation of the low-frequency (LF) field [55,56].…”

On the Fer expansion: Applications in solid-state nuclear magnetic resonance and physics

“…The authors obtained various bounds for Fer (ξ = 0.8604065) and Magnus (ξ = 1.086869) expansions. These results widen the range ξ = 0.628 originally given by Fer [88], and the range ξ = 0.693147 given by Pechukas and Light regarding the Magnus expansion [248].…”

“…The Bloch-Siegert shift can be seen by watching the motion of the red dot on the pot cover when the pot cover is rotating around an axis along the surface of the table that is quickly rotating. Saiko and Fedoruk [248] recently outlined that the Bloch-Siegert effect can also give rise to variations important for the operation of quantum computers [274] and also because of the interference of the counter-rotating electromagnetic-field components, the Bloch-Siegert effect provides a wonderful opportunity to measure not only the amplitude, but also the absolute phase of a monochromatic electromagnetic field [275].…”