Quantum logic gates using coherent population trapping states

Abstract

A scheme is proposed for achieving a controlled phase gate using interaction between atomic spin dipoles. Further, the spin states are prepared in coherent population trap states (CPTs), which are robust against perturbations, laser fluctuations etc. We show that one-qubit and two-qubit operations can easily be obtained in this scheme. The scheme is also robust against decoherences due to spontaneous emissions as the CPT states used are dressed states formed out of Zeeman sublevels of ground states of the bare atom. However, certain practical issues are of concern in actually obtaining the scheme, which are also discussed at the end of this paper.Conventional computers handle information in the form of bits -which take up values 0 or 1. Quantum computers on the other hand, use quantum bits (qubits), which can be prepared in states 0, 1 or any superposition of the two. Algorithms of quantum computation exploit this unique feature of quantum mechanical system to solve certain class of computational problems with lesser number of steps [1]. Hence there is a race to produce a reliable, robust and scalable quantum mechanical system which can be used as gates for quantum logic. There have been several attempts in the past to prepare such a system, using NMR of large molecules, quantum dot structures, ions in linear traps or neutral atoms in optical lattices [2,3], each system with its own benefits and drawbacks. One of the major requirement for designing a QC system is that they should be robust and reliable while interactions between any two of them should be on-demand. One such system is proposed here which involves neutral atoms prepared in coherent population trap (CPT) states. It is shown in this paper that such systems can be easily prepared and manipulated and it is possible to build onequbit and two-qubit gates using them. Since CPT states are 'dark states' of the atom-light interaction, the atoms prepared in such states will not interact with the light any more [4,5]. They will not evolve in time also, since they are already eigenstates of the full Hamiltonian that consist of atomic as well as interaction terms.

Robust atomic states for quantum information with continuous variables

“…The interaction leads to a dressed state that is a combination of all three ground states in such a way that it can be mapped to a state of the form |ψ〉 = sin(θ/2)|0〉 + exp(iϕ) cos(θ/2)|1〉. We have earlier shown that a discrete gate operation can be performed using this system (Vudayagiri, 2011). Here, we show that the same system can be used to perform continuous state preparation and, therefore, continuous operations as well.…”

“…When both the π and σ lasers are simultaneously present in Figure 1, the system goes into a unique eigenstate involving all three states, which is of interest to the rest of the communication (Vudayagiri and Tewari, 2006;Vudayagiri, 2011). This unique state is the dressed state of the six-state Hamiltonian,…”

“…The interaction would lead to a steady state and redistribution of the atoms. Following the formation of a controlled-phase gate, as described in Vudayagiri (2011), this phenomenon could be used in a "continuous" phase-gate, in a fashion similar to analog computation.…”