QUANTUM STATE TOMOGRAPHY THROUGH PHASE-SENSITIVE AMPLIFICATION

Abstract

The phase-sensitive linear amplification has been exploited for the tomographic reconstruction of single as well as multimode entangled fields. For the phase-sensitive amplification of a single mode cavity field both the correlated emission laser (eEL) and the driven three-level atomic system are used as amplifiers. A eEL amplifier amplifies both the quadratures of the field equally but introduces an unequal amount of noise in them. In this amplifier, the added noise in one of the quadratures of the field is quenched at the expense of enhanced noise in the conjugate quadrature. The noise-free quadrature of the amplified field is measured by using a balanced homo dyne detector (BHD). A one-to-one correspondence, in between the phase of the atomic coherence in eEL amplifier and the phase of the local oscillator (LO) used in the BHD, helps to record the noise-free quadrature of the field for a set of its phases. The measured quadrature distribution is then used to reconstruct the vVigner distribution of the field by using inverse Radon transformation. It is shown that in the limits of strong enough squeezing and sufficiently large gain the Wigner distribution of the initial field is recovered. This model has been applied to a Schrodinger-cat state and the Wigner function of its initial state is successfully reconstructed after its amplification through a two-photon eEL amplifier. In a driven three-level atomic system amplifier t he atomic coherence in between the upper and the lower levels is produced by an external driving field. This system exhibits a range of interesting behaviour depending upon the strength of external driving field. For a weak driving field this system acts as a phase-insensitive amplifier whereas, it behaves as a perfact degenerate parametric amplifier at the other extream of the driving field strength. In the parametric limit of its operation, this system quenches added noise from both the quadratures of the field however, one of the quadratures gets amplification at the cost of deamplification in the conjugate one. The amplified field quadrature is measured by using a BHD. A one-to-one correspondence in between the phase of the external driving field and the phase of the LO, helps to record the field quadrature with optimum gain over a set of its phases. The measured quadrature distribution is then used to reconstruct the Wigner function of the original field. This model is also applied to reconstruct the vVigner function of a Schrodinger-cat state. For a multimode entangled state of a cavity field two cases of interest are discussed. In the first case, the cavity modes are defined in terms of different frequency components and in the other case, the field modes consist of two orthogonal polarization states. In both these cases the cavity field is amplified by using eEL amplifiers. The measurement of the amplified field, consisting of different frequency components, is realized by seperating it out into its frequency components such that each frequency component is measured at a seperate set of BHD. However, for the measurement of a bimode field, having the same frequency, a single set of BHD is quite suffice. In this case the amplified field is first passed through a polarizer and then through a phase-shifter before its detection through a BHD. This arrangement helps to record the joint quadrature distribution of the bimode field. The measured quadrature distributions of both these fields are then used to reconstruct the Wigner functions of the fields. It is shown that for sufficiently large squeezing and for large enough gain in each mode of the field the Wigner functions of the initial states are successfully recovered.