Bloch-Siegert shift
Encyclopedia
The Bloch-Siegert shift is a phenomenon in quantum physics that becomes important for driven two-level systems when the driving gets strong (e.g. atoms driven by a strong laser drive or nuclear spins in NMR, driven by a strong oscillating magnetic field).
When the rotating wave approximation
(RWA) is invoked, the resonance between the driving field and a pseudospin occurs when the field frequency
is identical to the spin's transition frequency 
. The RWA is, however, an approximation. In 1940 Bloch and Siegert showed that the dropped parts oscillating rapidly can give rise to a shift in the true resonance frequency of the dipoles.
, a linearly polarized field is considered as a superposition of two circularly polarized fields of the same amplitude rotating in opposite directions with frequencies 
. Then, in the rotating frame(
), we can neglect the counter-rotating field and the Rabi frequency
is
), the effective precession frequency is
Then the resonance frequency is given by
and there are two solutions
and
The shift from the RWA of the first solution is dominant, and the correction to
is known as the Bloch-Siegert shift:
When the rotating wave approximation
Rotating wave approximation
The rotating wave approximation is an approximation used in atom optics and magnetic resonance. In this approximation, terms in a Hamiltonian which oscillate rapidly are neglected. This is a valid approximation when the applied electromagnetic radiation is near resonance with an atomic resonance,...
(RWA) is invoked, the resonance between the driving field and a pseudospin occurs when the field frequency
is identical to the spin's transition frequency . The RWA is, however, an approximation. In 1940 Bloch and Siegert showed that the dropped parts oscillating rapidly can give rise to a shift in the true resonance frequency of the dipoles.Rotating wave approximation
In RWA, when the perturbation to the two level system is, a linearly polarized field is considered as a superposition of two circularly polarized fields of the same amplitude rotating in opposite directions with frequencies . Then, in the rotating frame(), we can neglect the counter-rotating field and the Rabi frequencyRabi frequency
The Rabi frequency is the frequency of population oscillation for a given atomic transition in a given light field. It is associated with the strength of the coupling between the light and the transition. Rabi flopping between the levels of a 2-level system illuminated with resonant light, will...
is
Bloch-Siegert shift
Consider the effect due to the counter-rotating field. In the counter-rotating frame(), the effective precession frequency isThen the resonance frequency is given by
and there are two solutions
and
The shift from the RWA of the first solution is dominant, and the correction to
is known as the Bloch-Siegert shift: