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arXiv:1306.2132

All-optical reversible logic gate via adiabatic population transfer

Grigoryan, G., V. O. Chaltykyan, E. A. Gazazyan, O. Tikhova, Thomas Halfmann

Published Jun 10, 2013• 0 citations
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Abstract

The Toffoli gate is an essential logic element, which permits implementation of a reversible processor. It is of relevance both for classical as well as quantum logics. We propose and theoretically study all-optical implementations of three-bit and four-bit Toffoli gates by application of adiabatic population transfer techniques. For a three-bit Toffoli gate we use variants of stimulated Raman adiabatic passage (STIRAP) processes in a $Λ$-type level scheme, driven by two laser pulses at sufficiently large detunings. For the implementation of a four-bit Toffoli gate, we apply reversible adiabatic population transfer in five-level quantum systems, interacting with three laser pulses. We demonstrate correct all-optical implementation of the truth table of three-bit and four-bit Toffoli gates. Moreover, we derive conditions for adiabatic evolution of the population dynamics and robust operation of the gates.

DOI
10.48550/arxiv.1306.2132

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The Toffoli gate is an essential logic element, which permits implementation of a reversible processor. It is of relevance both for classical as well as quantum logics. We propose and theoretically study all-optical implementations of three-bit and four-bit Toffoli gates by application of adiabatic population transfer techniques. For a three-bit Toffoli gate we use variants of stimulated Raman adiabatic passage (STIRAP) processes in a ΛΛΛ-type level scheme, driven by two laser pulses at sufficiently large detunings. For the implementation of a four-bit Toffoli gate, we apply reversible adiabatic population transfer in five-level quantum systems, interacting with three laser pulses. We demonstrate correct all-optical implementation of the truth table of three-bit and four-bit Toffoli gates. Moreover, we derive conditions for adiabatic evolution of the population dynamics and robust operation of the gates.
We propose a robust scheme, using tripod stimulated Raman adiabatic passage, to generate one-qubit rotation gate. In this scheme, a four-level atom interacts with three resonant laser pulses and time evolution of the corresponding coherent system is designed such that the rotation gate is implemented at the end of process. Rotation angle in this gate is holonomic and has a geometrical basis in the parameter space. We also explore the effect of spontaneous emission on the population transfer with numerical solution of Schrödinger and Liouville equations.
In digital circuits, a Flip-Flop (FF) is a circuit element that has two stable states which can be used to store and remember state information. The state of the circuit can be changed by applying signals to the control input. FFs are the basic building blocks of sequential logic circuits, as logic gates AND,OR, NOT are the basic building block for combinational logic circuits, and are therefore necessary for any computations involving memory. Consequently, the design and implementation of FFs can be considered as a pre-requisite for memory machine design. Here we present the design of an optical FFs in an atomic multi-level system, based on the optical manipulation of populations and coherences using stimulated Raman adiabatic passage. We first demonstrate that both populations and coherences can be transferred over multistate systems. We then propose the design of toggle-FFs, Delay-FFs, and Serial-in Serial-Out (SISO) shift registers using such systems. For the design of the filp-flops we use a three level ΛΛΛ-type system. In order to design SISO shift registers we concatenate two ΛΛΛ-type systems and construct an "M"-type scheme, and similarly concatenating three ΛΛΛ-type system we are able to obtain a seven level system. By concatenating we are able to use output of one three level ΛΛΛ-type system serve as input of another three level ΛΛΛ-type system. On top of using populations for design of logic gates, we uniquely exploit the coherences for logic machine, which provides an additional degree of freedom which can be used for the design of computing elements.
The basic technique of stimulated Raman adiabatic passage for laser-induced adiabatic population transfer between discrete quantum states of an asymmetric double quantum well has been used in our study. The results show that the proper time-delay, overlap, and detuning of two pulses allows the coherent transfer between the states of a double quantum well system, leading to the possibility of implementation of semiconductor–based quantum logic gates and high efficiency optical switches. The impact of phase relaxation on the population transfer efficiency is also studied.