We study the sensitivity and resolution of phase measurement in a Mach-Zehnder interferometer with two-mode squeezed vacuum (n photons on average). We show that super-resolution and subHeisenberg sensitivity is obtained with parity detection. In particular, in our setup, dependence of the signal on the phase evolvesn times faster than in traditional schemes, and uncertainty in the phase estimation is better than 1/n.PACS numbers: 07.60. Ly, 95.75.kK, 42.50.St Different physical mechanisms contribute to phase measurement. Thus, measuring phase provides insight into a number of physical processes. Therefore, improved phase estimation benefits multiple areas of scientific research, such as quantum metrology, imaging, sensing, and information processing. Consequently, enormous efforts have been devoted to improve the resolution and sensitivity of interferometers. Sensitivity is a measure of the uncertainty in the phase estimation, while resolution is rate at which signal changes with changing phase.In what follows, we direct our attention to quantum interferometry. The benchmark that quantum interferometry is compared against is one with coherent light input and intensity difference measurement at the output of a Mach-Zehnder interferometer (MZI). In general, phase sensitivity of this benchmark is shot-noise limited, namely ∆ϕ = 1/ √n , wheren is the average number of photons. However, better sensitivity is possible if nonlinear interaction between photons in the MZI takes place [1]. In what follows, we only consider phase accumulation due to linear processes.In 1981, Caves pointed out that by using coherent light and squeezed vacuum one could beat the shot-noise limit ∆ϕ < 1/ √n (super-sensitivity) [2]. In the work of Boto et al., it was shown that by exploiting quantum states of light, such as N00N states, it is possible to beat the Rayleigh diffraction limit in imaging and lithography (super resolution) while also beating the shot-noise limit in phase estimation [3,4,5,6]. Finally, it was shown in Ref.[7] that input state entanglement is important in order to achieve super-sensitivity in a linear interferometer.non-classical light Experimental realization of these predictions have been hindered by the fact that entangled states of light, with large numbers of photons, are difficult to obtain. Therefore we turn our attention to the brightest (experimentally available) nonclassical light -two-mode squeezed vacuum (TMSV). A state of TMSV is a superposition of twin Fock states |ψn = ∞ n=0 p n (n) |n, n , where the probability of a twin Fock state |n, n = |n A |n B to be present de- pends on average number of photons in both modes of TMSV,n, in the following way p n (n) = (1 − tn)t n n with tn = 1/ (1 + 2/n) [8].Light entering a MZI in TMSV state exits a lossless interferometer in the state |ψ f =Û MZI |ψn , where the MZI is described by the unitary transformation U MZI (Fig. 1). This transformation, in terms of the field operators for the optical modesâ andb, isÛ MZI =ÛP ϕÛ = exp ϕ â †b −b †â /2 , wherê P ϕ =exp −...
