Nonlinear interferometer as a resource for maximally entangled photonic states: Application to interferometry

Abstract

Nonlinear interferometers are Mach-Zehnder interferometers with Kerr media in either one or both arms. We refer to these devices, respectively, as the asymmetric and symmetric nonlinear interferometers. In the asymmetric case, with one input mode in the vacuum, it is possible to generate maximally entangled photonic states or superpositions of such states. We consider the device as a resource of entangled states for applications to Heisenberg-limited interferometry. Interferometry with the maximally entangled states cannot be performed by simply subtracting the output photocounts as in standard interferometry. Instead, one must perform parity measurements on only one of the output beams. We show that the symmetric nonlinear interferometer, with one input mode in the vacuum, may be used to perform such parity measurements. The same device is shown to produce, with an input coherent state and upon projective measurements, even or odd coherent states, examples of the Schrödinger-cat states.

Quantum metrology for nonlinear phase shifts with entangled coherent states

“…An important case of entangled coherent states are the two-mode path entangled states, a state analogous to a NOON state, but with one of two modes containing a coherent state rather than a Fock state [26]. This particular ECS can be represented as a superposition of NOON states with different photon numbers [25]. Using linear optical elements, the phase sensitivity of ECSs outperforms that of NOON and bat states [30], both without [25][26][27] and with losses [28], because coherent states maintain their properties in the presence of loss.…”

“…Entangled coherent states (ECSs) [17][18][19][20][21][22][23][24] are also able to do this [25][26][27] and can outperform that of NOON states in the region of very modest particle numbers with a linear phase operation [28,29]. An important case of entangled coherent states are the two-mode path entangled states, a state analogous to a NOON state, but with one of two modes containing a coherent state rather than a Fock state [26].…”

“…This particular ECS can be represented as a superposition of NOON states with different photon numbers [25]. Using linear optical elements, the phase sensitivity of ECSs outperforms that of NOON and bat states [30], both without [25][26][27] and with losses [28], because coherent states maintain their properties in the presence of loss. Given all this recent work, a natural question arises regarding comparison of the phase enhancement for ECSs, compared to NOON and other states, in the case of non-linear phase shifts [7].…”

Bell-inequality tests using asymmetric entangled coherent states in asymmetric lossy environments

“…Entangled coherent states (ECSs) in free-traveling fields [1][2][3] have been found to be useful for various applications such as Bell inequality tests [4][5][6][7][8][9][10][11][12][13][14][15][16][17], tests for non-local realism [18,19], quantum teleportation [20][21][22][23][24], quantum computation [25][26][27][28][29][30][31], precision measurements [32][33][34][35][36][37][38][39], quantum repeater [40] and quantum key distribution [41]. The ECSs can be realized in various systems that can be described as harmonic oscillators and numerous schemes for their implementing have been suggested [1][2][3][42][43][44][45]…”

Atom-mediated effective interactions between modes of a bimodal cavity

“…al [3]. A different approach to produce those states is to use a nonlinear Hamiltonian [16][17][18][19][20]. This method involves Kerr-like Hamiltonians and the superposition states are created from the evolution of initial coherent states.…”