
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
Nuclear magnetic resonance (NMR) is a physical phenomenon in which atomic nucleus, nuclei in a strong constant magnetic field are disturbed by a weak oscillating magnetic field (in the near and far field, near field) and respond by producing ...
, 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
Felix Bloch
Felix Bloch (; ; 23 October 1905 – 10 September 1983) was a Swiss-American physicist who shared the 1952 Nobel Prize in Physics with Edward Mills Purcell "for their development of new methods for nuclear magnetic precision measurements and di ...
and Arnold Siegert showed that the dropped parts oscillating rapidly can give rise to a shift in the true resonance frequency of the dipoles.
The Bloch–Siegert shift has been used for practical purposes in both NMR and
MRI
Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to generate pictures of the anatomy and the physiological processes inside the body. MRI scanners use strong magnetic fields, magnetic field gradients, and rad ...
, including power calibration, image encoding,
and magnetic field mapping.
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 frequency
The Rabi frequency is the frequency at which the Probability amplitude, probability amplitudes of two atomic electron transition, atomic energy levels fluctuate in an oscillating electromagnetic field. It is proportional to the transition dipole m ...
is
:
where
is the on-resonance Rabi frequency.
Bloch–Siegert shift
Consider the effect due to the counter-rotating field. In the counter-rotating frame (
), the effective detuning is
and the counter-rotating field adds a driving component perpendicular to the detuning, with equal amplitude
.
The counter-rotating field effectively
dresses
A dress (also known as a frock or a gown) is a one-piece outer garment that is worn on the torso, hangs down over the legs, and is primarily worn by women or girls. Dresses often consist of a bodice attached to a skirt.
Dress shapes, silhoue ...
the system, where we can define a new quantization axis slightly tilted from the original one, with an effective detuning
:
Therefore, the resonance frequency (
) of the system dressed by the counter-rotating field is
away from our frame of reference, which is rotating at
:
and there are two solutions for
: