Adiabatic Mach-Zehnder Interferometry on a Quantized Bose-Josephson Junction

We propose a scheme to achieve Mach-Zehnder interferometry using a quantized Bose-Josephson junction with a negative charging energy. The quantum adiabatic evolution through a dynamical bifurcation is used to accomplish the beam splitting and recombination. The negative charging energy ensures the existence of a path-entangled state which enhances the phase measurement precision to the Heisenberg limit. A feasible detection procedure is also presented. The scheme should be realizable with current technology.

Figure 1

The energy spectra and the ground states for a symmetric quantized Bose-Josephson junction with $E_C=-2.0$ and $N=20$. (a) The energy spectra for different $T$. (b), (c) The degenerated first excited state $|1⟩$ and the ground state $|0⟩$ for $T=0$. (d) The ground state for $T=40$.

Figure 2

The beam splitting process from $T=40$ to $T=0$ in a symmetric [cases (a–(c)] or weakly asymmetric (case d) quantized Bose-Josephson junction with $E_C=-2.0$ and $N=20$. (a) The initial state at $T=40$ is the ground state. (b) The destination state at $T=0$ is a path-entangled state $(|10,-10⟩+|10,+10⟩)/\sqrt{2}$. (c) The fidelities of the evolving states $\Psi (T)$ versus the coupling $T$. (d) The maximum fidelity $F_{\Phi }^{\max }=\max (|⟨\Phi (\phi )|\Psi (T=0,\delta )⟩{|}^2)$ of the destination state $\Psi (T=0,\delta )$ to the path-entangled state $|\Phi (\phi )⟩$ vs the imbalance $\delta$.

Figure 3

Behaviors of Mach-Zehnder interference in the output states of a symmetric quantized Bose-Josephson junction with $N=20$ and $E_C=-2.0$ with initial states $|\Phi (\varphi )⟩$ through a dynamical bifurcation to the strong coupling limit ($T=40$).

Figure 4

The energy spectrum, the states $|0⟩$ and $|1⟩$, and their fidelities to the symmetric counterparts for an asymmetric quantized Bose-Josephson junction with $N=20$, $E_C=-2.0$, and $\delta =0.5$. (a) The energy spectrum. (b) The fidelities $F_{{00}^{\prime }}$ and $F_{{11}^{\prime }}$ for different $T$. (c) The ground state $|0⟩$ for $T=0$. (d) The first excited state $|1⟩$ for $T=0$.