Pis’ma v ZhETF, vol. 110, iss. 7, pp. 435 - 436
© 2019 October 10
Possibility of direct observation of the Bloch-Siegert shift in coherent
dynamics of multiphoton Raman transitions
A. P. Saiko+1), S. A. Markevich+, R. Fedaruk∗
+Scientific-Practical Material Research Centre, Belarus National Academy of Sciences, 20072 Minsk, Belarus
∗Institute of Physics, University of Szczecin, 70-451 Szczecin, Poland
Submitted 8 August 2019
Resubmitted 28 August 2019
Accepted 28
August 2019
DOI: 10.1134/S0370274X19190019
Modern studies of the resonant matter-light inter-
We use the semi-classical Rabi model and the non-
action evolve toward the ultrastrong coupling regime
secular perturbation theory based on the Bogoliubov
where the coupling strength is comparable to the tran-
averaging method [37]. We show that the co-rotating
sition frequency of a two-level system (qubit). The ro-
component of the low-frequency modulation field excites
tating wave approximation (RWA) is broken and the
virtual multiple photon processes between the dressed
contribution of the counter-rotating (non-RWA) terms
states and forms the Rabi frequency in the RWA. The
to the coupling Hamiltonian must be taken into account
counter-rotating modulation component also gives a sig-
[1-4]. The well-known manifestation of the non-RWA
nificant contribution to the Rabi frequency owing to the
terms is the Bloch-Siegert effect [5].
Bloch-Siegert effect. It is shown that for properly cho-
The ultrastrong regime is extremely important for
sen parameters of the modulation field and qubit, the
quantum information processing [6] and is widely stud-
Rabi oscillations in the RWA vanish due to destruc-
ied for various quantum objects [6-9]. In this regime,
tive interference of multiple photon processes (Fig. 1).
the Rabi oscillations have been investigated [10-22]. The
In this case the Rabi oscillation results exclusively from
dressing of qubit by the resonant electromagnetic field
the Bloch-Siegert effect and is directly observed in the
gives rise to new energy levels of the coupled field-qubit
time-resolved coherent dynamics as the Bloch-Siegert
system and the Rabi frequency characterizes the split-
oscillation. Correspondingly, in Fourier spectra of the
ting of each bare level [7]. The second field with the
coherent response, triplets are transformed into doublets
frequency closed to the Rabi frequency excites effec-
with the splitting between the lines equal to twice the
tively transitions between the dressed states. This phe-
Bloch-Siegert shift. We demonstrate these features by
nomenon, called the Rabi resonance, has been observed
calculations of the qubit’s evolution in the conditions
in electron paramagnetic resonance [23-25], NMR [26,
of experiments with a NV center in diamond. The di-
27] and in optics [28, 29]. The ultrastrong regime and
rect observation of the Bloch-Siegert oscillation offers
the Bloch-Siegert effect becomes significant in the co-
new possibilities for studying driven quantum systems
herent dynamics of the doubly dressed states [24, 25, 30].
in the ultastrong regime. Non-RWA effects of atom-bath
This dynamics finds applications in quantum informa-
interactions [38] and propositions of two-photon Raman
tion technologies [31, 32] and radio-frequency magne-
transition for a heat-powered maser [39] are mentioned.
tometry [33]. Additional multiphoton resonances occur
Full text of the paper is published in JETP Letters
at the subharmonics of the Rabi frequency [28, 34].
journal. DOI: 10.1134/S0021364019190019
Recently, so-called Floquet Raman transitions at mul-
1. Y. Yan, Z. Lü, and H. Zheng, Phys. Rev. A 91, 053834
tiphoton Rabi resonances have been observed for NV
(2015).
center in diamond driven by the amplitude-modulated
2. X. Cao, J. Q. You, H. Zheng, A. G. Kofman, and F. Nori,
microwave field [35]. It was shown [36] that the ultra-
Phys. Rev. A 82, 022119 (2010).
strong regime is reached in [35] resulting in the signifi-
3. I. D. Feranchuk and A. V. Leonov, Phys. Lett. A 375,
cant Bloch-Siegert shift. Here, we propose the method
385 (2011).
for direct observation of the Bloch-Siegert oscillation in
4. F. Angaroni, G. Benenti, and G. Strini, Eur. Phys. J. D
the coherent dynamics of the second-order Raman tran-
72, 32109 (2018).
sition.
5. F. Bloch and A. Siegert, Phys. Rev. 57, 522 (1940).
6. T. Takui, L. Berliner, and G. Hanson, Electron Spin Res-
onance (ESR) Based Quantum Computing, Springer,
1)e-mail: saiko@physics.by
N.Y. (2016).
Письма в ЖЭТФ том 110 вып. 7 - 8
2019
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