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The Journal of Chemical Physics

Computational investigation and experimental considerations for the classical implementation of a full adder on SO2 by optical pump-probe schemes

L. Bomble, B. Lavorel, F. Remacle, Michèle Desouter-Lecomte

Published May 20, 2008• 4 citations
Publisher

Abstract

Following the scheme recently proposed by Remacle and Levine [Phys. Rev. A 73, 033820 (2006)], we investigate the concrete implementation of a classical full adder on two electronic states (X 1A1 and C 1B2) of the SO2 molecule by optical pump-probe laser pulses using intuitive and counterintuitive (stimulated Raman adiabatic passage) excitation schemes. The resources needed for providing the inputs and reading out are discussed, as well as the conditions for achieving robustness in both the intuitive and counterintuitive pump-dump sequences. The fidelity of the scheme is analyzed with respect to experimental noise and two kinds of perturbations: The coupling to the neighboring rovibrational states and a finite rotational temperature that leads to a mixture for the initial state. It is shown that the logic processing of a full addition cycle can be realistically experimentally implemented on a picosecond time scale while the readout takes a few nanoseconds.

DOI
10.1063/1.2920486

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Following the scheme recently proposed by Remacle and Levine [Phys. Rev. A 73, 033820 (2006)], we investigate the concrete implementation of a classical full adder on two electronic states (X 1A1 and C 1B2) of the SO2 molecule by optical pump-probe laser pulses using intuitive and counterintuitive (stimulated Raman adiabatic passage) excitation schemes. The resources needed for providing the inputs and reading out are discussed, as well as the conditions for achieving robustness in both the intuitive and counterintuitive pump-dump sequences. The fidelity of the scheme is analyzed with respect to experimental noise and two kinds of perturbations: The coupling to the neighboring rovibrational states and a finite rotational temperature that leads to a mixture for the initial state. It is shown that the logic processing of a full addition cycle can be realistically experimentally implemented on a picosecond time scale while the readout takes a few nanoseconds.
Stimulated Raman adiabatic passage (STIRAP) is a well-studied pump-probe control scheme for manipulating the population of quantum states of atoms or molecules. By encoding the digits to be operated on as ``on'' or ``off'' laser input signals we show how STIRAP can be used to implement a finite-state logic machine. The physical conditions required for an effective STIRAP operation are related to the physical conditions expected for a logic machine. In particular, a condition is derived on the mean number of photons that represent an on pulse. A finite-state machine computes Boolean expressions that depend both on the input and on the present state of the machine. With two input signals we show how to implement a full adder where the carry-in digit is stored in the state of the machine. Furthermore, we show that it is possible to store the carry-out digit as the next state and thereby return the machine to a state ready for the next full addition. Such a machine operates as a cyclical full adder. We further show how this full adder can equally well be operated as a full subtractor. To the best of our knowledge this is the first example of a nanosized system that implements a full subtraction.
The interaction of two narrow band (Δν<100 MHz) UV light pulses of different intensity with a molecular three-level system is investigated experimentally. The laser frequencies are tuned to an up (pump) and a down (dump) transition sharing a common excited rovibronic S1 level whose population is probed by a transition to the ionization continuum and ion detection. The time sequence of the two pulses results either in a lambda type coherent stimulated Raman adiabatic passage or a stimulated emission pumping (SEP) process. When the first case is realized by a 6.4 ns delay of the low intensity pump laser from the high intensity dump laser pulse, a fourfold increase of the depth of the ion dips compared to the SEP experiment is observed. This is in line with numerical calculations of the level populations using a density matrix formalism including coherent effects. Rotationally resolved ion dip spectra of the 62 state of benzene are presented and demonstrate the high sensitivity of the coherent excitation process of this work for ion dip spectroscopy.
Within the context of vibrational molecular quantum computing, we investigate the implementation of a full addition of two binary digits and a carry that provides the sum and the carry out. Four qubits are necessary and they are encoded into four different normal vibrational modes of a molecule. We choose the bromoacetyl chloride molecule because it possesses four bright infrared active modes. The ground and first excited states of each mode form the one-qubit computational basis set. Two approaches are proposed for the realization of the full addition. In the first one, we optimize a pulse that implements directly the entire addition by a single unitary transformation. In the second one, we decompose the full addition in elementary quantum gates, following a scheme proposed by Vedral et al. [Phys. Rev. A 54, 147 (1996)]. Four elementary quantum gates are necessary, two two-qubit CNOT gates (controlled NOT) and two three-qubit TOFFOLI gates (controlled-controlled NOT). All the logic operations consist in one-qubit flip. The logic implementation is therefore quasiclassical and the readout is based on a population analysis of the vibrational modes that does not take the phases into account. The fields are optimized by the multitarget extension of the optimal control theory involving all the transformations among the 2(4) qubit states. A single cycle of addition without considering the preparation or the measure or copy of the result can be carried out in a very competitive time, on a picosecond time scale.
The implementation of a quantum-controlled full adder-subtractor of two binary digits and of a "carry in" or a "borrow in" is simulated by encoding four qubits in the vibrational eigenstates of a tetra-atomic molecule (trans-HONO). The laser field of the gate is computed using optimal control theory by treating dynamics in full dimensionality. A controlled qubit enforces the addition or the subtraction. The global unitary transformation that connects the inputs to the outputs is driven by a single laser pulse. This decreases the duration of the operation and allows for a better use of the optical resources and for an improvement of the fidelity (>97%). Initialization and reading out are discussed. The timescale of the sequence initialization, gate and read out is<100 ps.
The expansion of laser cooling capabilities from the atomic to the molecular regime has proven challenging due to the lack of availability of an equivalent closed-loop cooling cycle within the rich molecular internal energy level structure. An enticing solution is the application of ultrafast coherent control techniques to ultracold molecule generation. Unlike continuous-wave photoassociation techniques, the use of broadband 'pump' and 'dump' pulses offers the opportunity to access deeply bound vibrational states. Unlike alternative vibrational cooling strategies such as stimulated Raman adiabatic passage or incoherent optical cycling, this approach preserves coherence and does not require a detailed knowledge of the system spectroscopy. We report on pump-probe experiments investigating the dynamical evolution of bound excited-state Rb2dimers after photoassociation. Learning about these dynamics is an important step towards efficient pump-dump formation of deeply bound ground-state molecules. Based on a spectroscopic measurement of the initial state occupied by the interacting atom pairs, we provide evidence that background triplet molecules preassociated by the trapping lasers, additionally to unbound scattering atom pairs, may play an important role in photoassociation dynamics.