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 ΔM of the lasers, Δϕ ×ΔM >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.