Triple quantum nutation in the two-level NMR system in the rotating frame

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...

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confidence: 73%

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confidence: 84%

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

Saǐko

Fedoruk

2008

“…and electron spins, double-well quantum dots, flux and charge qubits in superconducting systems. In NMR [6,7], EPR [5,8,9] and optical resonance [10] such investigations are used in the development of line-narrowing methods.…”

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confidence: 99%

“…The results of studies of qubits dressed by bichromatic radiation formed by fields with strongly different frequencies are important for a wide range of physical objects, including, among others, nuclear and electron spins, double-well quantum dots, flux and charge qubits in superconducting systems. In NMR [6,7], EPR [5,8,9] and optical resonance [10] such investigations are used in the development of line-narrowing methods.…”

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confidence: 99%

Multiplication of qubits in a doubly resonant bichromatic field

Saǐko

Fedaruk

2010

Multiplication of spin qubits arises at double resonance in a bichromatic field when the frequency of the radio-frequency (rf) field is close to that of the Rabi oscillation in the microwave field, provided its frequency equals the Larmor frequency of the initial qubit. We show that the operational multiphoton transitions of dressed qubits can be selected by the choice of both the rotating frame and the rf phase. In order to enhance the precision of dressed qubit operations in the strong-field regime, the counter-rotating component of the rf field is taken into account.PACS: 03.67. Pp, 33.40.+f, 33.35.+r Theoretical models of quantum computations assume the existence of an ideal two-level quantum system (qubit) and the possibility of an exact description of the qubit's interaction with external electromagnetic fields [1]. It is known that the resonant interaction between electromagnetic radiation and qubit induces Rabi oscillations, which are the basis for quantum operations.The Rabi frequency ω R is defined by the amplitude of the electromagnetic field and usually is much smaller than the energy difference ω 0 (in frequency units) between the qubit's states.The "dressing" of qubit by the electromagnetic field splits each level into two giving rise to two new qubits with energy difference ω R . The spectrum of the multilevel "qubit + field" system consists of three lines at the frequencies ω 0 and ω 0 ± ω R (the Mollow triplet [2]). The second low-frequency electromagnetic field with the frequency close to the Rabi frequency ω R could induce an additional Rabi oscillation on dressed states of new qubits. These qubits are attracting interest because their coherence time is longer than that of the initial qubit [3 -5]. The results of studies of qubits dressed by bichromatic radiation formed by fields with strongly different frequencies are important for a wide range of physical objects, including, among others, nuclear

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confidence: 99%

Effective field and the Bloch-Siegert shift at bichromatic excitation of multiphoton EPR

Saǐko¹,

Fedoruk²,

Markevich³

2006

In view of the possibilities for changing the energy states of the quantum state with external electromagnetic fields and its interaction with the environment, interest in studying the dynamics of multiphoton processes in nonlinear optics, NMR and EPR, has increased recently [1][2][3][4][5][6][7][8]. In two-level spin systems, there are no real intermediate levels, and "dressed" spin systems formed by external electromagnetic fields can serve as intermediate levels. In view of this circumstance, a multilevel dynamical quantum system with controllable properties can be created on the basis of the two-level system. Analysis of the dynamics of the dressed spin systems opens new perspectives for developing methods in order to narrow spectral lines, to separate overlapping spectra, and to increase the existence time of coherent spin states.In pulsed EPR experiments based on the simultaneous absorption or emission of several photons with noticeably different frequencies, e.g., microwave and RF radiation, two-and three-photon electron spin echo [1], two-photon nutation [7], as well as RF-fieldinduced transparency [3] and nutation on dressed states [4,5], were observed. Owing to the small amplitude of the effective field (effective Rabi frequency) of multiphoton transitions, as well as to the presence of inhomogeneous line broadening in real systems, difficulties remain both in direct observation of the dynamics of these transitions and in its quantitative interpretation on the basis of adequate theoretical approaches.In this work, the dynamics of multiphoton transitions in two-level spin systems with its excitation by bichromatic (transverse microwave and longitudinal RF) radiation is studied theoretically and experimentally. To this end, the nonstationary nutation phenomenon, which is present the dynamics of quantum transitions, is used. The nutation frequency is directly determined by the effective interaction field. The direct observation of the dynamics of the interaction of radiation with the spin system makes it possible to reveal regions of multiphoton transitions caused by the inhomogeneous broadening.In the semiclassical approximation, the Hamiltonian of the electron spin system (spin S = 1/2) in the linearly polarized microwave field directed along the x axis of the laboratory coordinate system, as well as in the linearly polarized RF and static magnetic fields directed along the z axis, can be written in the form (1) where ω 0 = γ B 0 is the resonance frequency of spin variables in the magnetic field B 0 , γ is the electron gyromagnetic ratio, ω 1 = γ B 1 and ω 2 = γ B 2 are the Rabi frequency, and B 1 , B 2 , ω mw , ω rf , ϕ , and ψ are the amplitudes, frequencies, and phases of the microwave and RF fields, respectively. The dynamics of multiphoton transitions in a two-level spin system excited by transverse microwave and longitudinal RF fields with the frequencies ω mw and ω rf , respectively, is analyzed. The effective time-independent Hamiltonian describing the "dressed" spin states of the "spin + bichro...