Quantum Precision Measurements

In quantum mechanics, measurement of non-commuting
observables (e.g. momentum and position of a particle) are limited with the
Heisenberg uncertainty principle (i.e. Δx×Δp ≥ *h*). Similarly in a laser (which is
almost in coherent state) signal to noise ratio (SNR) is proportional to the
number of lasing photons, *M*. The
precision of the measurement, made using this laser, is proportional to 1/*M*, which is called the standard quantum
limit (SQL). Hence, one needs to increase the number of photons to achieve
higher precision measurements. However, high number of photons equivalently
means a destructive measurement.

In quantum
optics, this difficulty is overcome using the notion of squeezed states. The
coherent states distribute the uncertainty between Δx and Δp (in
quantum optics E-field and B-field) in equal amounts. Similar relations hold
for the phase uncertainty Δϕ and photon number fluctuations Δ*M* of the lasers, Δϕ ×Δ*M* >1. On the other hand, using the
squeezed quantum states, one can squeeze the uncertainty in the E-field by
compromising a corresponding broadening in the knowledge of the B-field. So,
using squeezed states high precision measurements can be conducted by small amplitude
pulses.

Achievement of
squeezed states, however, necessitates nonlinear interactions among atoms and among
photons. Such interactions usually do not exist naturally and are hard to treat
analytically. Researchers can obtain such nonlinear interactions effectively,
by making the ensemble interact with a light pulse twice by scattering from a
mirror. Even though this is a fascinating achievement, it necessitates extra
care for design and space for the optical components.

In a recent study, we show that squeezed states of the ensemble atoms can be
achieved only with single interaction of light, if the light-atom interaction
Hamiltonian is chosen properly (off-diagonal in character). This is a major
achievement, which can be used in ongoing experimental setups for continually
squeezing of the sample. Therefore, it is expected to be widely used in
squeezing experiments.

In another work, we detect the spatial
position of a cantilever much more precisely by coupling it to a BEC. In atomic
force microscopy (AFM), the position of the tip is measured by directly
monitoring the displacement of the mechanical oscillator (cantilever) by the
deflection of the laser beam. In our setup, we monitor the motion of the cantilever indirectly by
conducting measurements on the BEC. Cantilever is coupled to the BEC
magnetically. Hence, its position changes the magnetic field and spin
polarization of the BEC. When the BEC spin state is squeezed (by interacting
with light), cantilever position can be measured much precisely and nondestructively.