Simulation of single-qubit gates in spin-orbit coupled Bose-Einstein condensate with cubic-quintic nonlinearity by nonlinear perturbations

Abstract

We consider spin-orbit coupled Bose-Einstein condensates with cubic-quintic nonlinear interaction within the framework of second quantization formulation and find eigen states using numerical simulation and mean-field approximation. We show that two low-lying Schrodinger cat states remain degenerate up to a certain value of Raman coupling strength and these states can serve as qubit basis. We take three different nonlinear perturbations and find that the perturbations can result in different rotations of qubit state on Bloch sphere. We calculate the unitary operator corresponding to each perturbation and suggest the possibilities for obtaining various gates in ultra-cold atomic system.

Figures (6)

• Figure 1: The ground state energy as a function of $k_0/N$ for the set of parameter values $u_0 = -3.35\times 10^{-6}, u_1= -2.85\times 10^{-3}, u_2 = 3.0\times 10^{-3}, N=500$ and ${p}_0= -1\times 10^{-6}$ obtained from exact calculation.
• Figure 2: The energy difference of low-lying excited states from the ground state as a function of $k_0/N$ for the set of parameter values $u_0 = -3.35\times 10^{-6}, u_1= -2.85\times 10^{-3}, u_2 = 3.0\times 10^{-3}, \delta=0, N=500$ and $p_{0}= -1\times 10^{-6}$ obtained from exact calculation.
• Figure 3: Probability distribution for the ground state as derived from mean-field theory as a function of spin-up atom number. $\Lambda=0.5$ (blue), $\Lambda=0.7$ (black), $\Lambda=0.9$ (red) and $\Lambda=0.998$ (green) for $N=500$.
• Figure 4: Variation of ground state energy $E_0$ as a function of $k_{0}/N$ derived from the Schrödinger cat states. The parameters taken are same as earlier: $u_0 = -3.35\times 10^{-6}, u_1= -2.85\times 10^{-3}, u_2 = 3.0\times 10^{-3}$ and $p_{0}= -1\times 10^{-6}$.
• Figure 5: Variation of the energy difference between two low-lying quasi degenerate energy levels as a function of $k_{0}/N$ derived from the Schrödinger cat states. The parameters taken are same as earlier: $u_0 = -3.35\times 10^{-6}, u_1= -2.85\times 10^{-3}, u_2 = 3.0\times 10^{-3}$ and $p_{0}= -1\times 10^{-6}$.