Physics 3, 38 (2010)

Viewpoint

Ultrafast computing with molecules

Ian WalmsleyClarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, UK

Published May 3, 2010

Vibrations of the atoms in a molecule are used to implement a Fourier transform orders of magnitude faster thanpossible with devices based on conventional electronics.

Subject Areas: Atomic and Molecular Physics, Quantum Information, Optics

A Viewpoint on:Ultrafast Fourier Transform with a Femtosecond-Laser-Driven MoleculeKouichi Hosaka, Hiroyuki Shimada, Hisashi Chiba, Hiroyuki Katsuki, Yoshiaki Teranishi, Yukiyoshi Ohtsuki andKenji OhmoriPhys. Rev. Lett. 104, 180501 (2010) – Published May 3, 2010

The intimate connection between information andphysics has received considerable emphasis in the pasttwo decades, in large part due to the stunning suc-cesses of quantum information science (QIS). This hasled to the exploration of a wide variety of physicalplatforms that may be adapted for implementing use-ful information-processing protocols. Among these areatoms, ions, molecules, photons, superconductors, andsemiconductors.

The focus of QIS is on capabilities for computing,communications, and metrology that transcend those ofdevices designed using principles of classical physics.The emergence of this field has led, in addition, to con-siderations of whether classical information processingmay be enhanced by making use of new physical in-stantiations, even when the full power of multiparticlequantum correlations are not used [1, 2]. Writing inPhysical Review Letters, Kouichi Hosaka [3] and collab-orators from several institutions in Japan illustrate howquantum interference may be used to execute a commonclassical algorithm very rapidly—within a few tens offemtoseconds. Hosaka et al. demonstrate that the dy-namics associated with the vibrations of the atoms ina molecule can be used to implement a Fourier trans-form. The rapidity of the molecular oscillations meansthat this protocol can be executed very quickly—muchquicker, as the authors point out, than any conceivabledevice based on conventional electronics.

The physics underlying the algorithm is simple andelegant. The vibrational mode of a diatomic molecule,when excited close to equilibrium, approximates an iso-lated harmonic oscillator. If the molecule is well isolatedfrom its environment, and at a low temperature, the os-cillator experiences very little decoherence either fromcollisions, or by the coupling of the vibrational and ro-tational motion, so that the unitary evolution necessaryfor the effect is dominant.

A remarkable feature of the quantum harmonic oscil-lator is that the dynamical evolution of a wave packetis exactly that of a fractional Fourier transform, withthe complete transform occurring periodically at timest = t0 + (2n + 1)π/2ω, (n = 0, 1, 2 . . .), where t0 is aninitial reference time. Therefore the wave packet one-quarter period after initial preparation is the Fouriertransform of the original wave packet:

ψ(x, t = t0 + π/2ω) ∝ ψ̃(p = mωx/h, t0). (1)

An alternative way to see this is in terms of a phase-space picture of the motion, as illustrated in Fig. 1 (a).

The Wigner function Wψ(x, p; t) of the wave packetprovides a convenient representation of its quantumstate, simultaneously encoding joint information aboutthe position x and momentum p of the oscillator. It is ajoint quasiprobability density function, the marginals ofwhich are the probability distributions of the particle’sposition or momentum. This function follows a circu-lar trajectory through the phase space of the oscillator,as indicated in the Fig. 1, and the dynamics are simplydescribed by rotations of the Wigner distribution aboutthe origin.

It is clear from this picture that a measurement of theposition of the oscillator, indicated by the projection ofthe Wigner function onto the position axis of the phasespace, will transform between that of the initial positiondistribution and the initial momentum distribution ev-ery quarter period. This feature has been recognized asenabling a number of useful applications. For example,the fractional Fourier transform implemented at timesbetween t and t = t0 + π/2ω suggests that sufficient in-formation can be obtained to completely reconstruct thequantum state of the oscillator [4, 5].

In the present paper, the authors now use these dy-namics to effect a discrete Fourier transform. A vibra-

DOI: 10.1103/Physics.3.38URL: http://link.aps.org/doi/10.1103/Physics.3.38

c© 2010 American Physical Society

Physics 3, 38 (2010)

FIG. 1: (a) Phase space dynamics of a molecular vibrationalharmonic oscillator. Time evolution is equivalent to a rotationof the phase space. The Wigner function representing the vi-brational quantum state is shown at two different times differ-ing by a quarter of the vibrational period. Measurement of theposition of the vibrational wave packet is equivalent to pro-jection of the Wigner function onto the coordinate axis. Thetwo marginal distributions shown (lines) indicate the origin ofthe Fourier transform, since they are proportional to the ini-tial probability distributions of the position and momentumprobability of the wave packet. (b) The diatomic molecule isexcited from the ground to the first excited electronic state bya shaped optical program pulse (P) that prepares the initialquantum state of the vibrational mode—effectively program-ming the distribution to be Fourier transformed. A quartervibrational period later, a reference pulse (R), generates a sec-ond vibrational wave packet that interferes with the first, con-verting the accumulated phase into populations of vibrationallevels in the excited state. A measurement laser (M) reads outthe populations by inducing transitions to a higher-lying elec-tronic state, from which fluorescence (f) is detected. The fluo-rescence intensity is proportional to the population in the vi-brational level to which the measurement laser is tuned. (Il-lustration: (a) Dane Austin; (b) Alan Stonebraker)

tional wave packet is generated in an iodine molecule byexciting the electronic transition to which the vibrationalmode is coupled. With the electron in the excited state,the atoms are no longer in equilibrium and begin to os-cillate. The vibrational quantum state can be adjustedby changing the temporal shape of the optical pulse thatexcites the electron—shaking the electron in a carefullycontrolled way enables the shape of the molecular vibra-tional wave packet to be sculpted.

The transformed wave packet is measured by meansof a two-step process [see Fig. 1 (b)]. First, a referencewave packet, generated in a similar manner to the pro-gram pulse by a separate reference laser pulse, is added.This has the effect of changing the amplitudes of the vi-brational eigenstates making up the wave packet in pro-portion to the phase they have accumulated in their freeevolution. The particular mechanism for this is that themolecular states may be excited or de-excited, depend-ing on the relative phase of the electronic dipole excitedby the first pulse with respect to the electric field of thesecond pulse. Once this phase-to-amplitude transfer hasoccurred, the amplitudes of the individual vibrationalstates are measured by exciting them to a higher elec-tronic state using a separate narrow band probe laser.The fluorescence from these states is measured as a func-tion of the wavelength of the probe laser and as a func-tion of the phase of the reference laser pulse. This givesthe eigenstate populations as the probe laser is tunedthrough the appropriate energy level, from which thephases may be inferred and the wave packet evolutiondetermined.

The authors point out the important feature that themolecular motion executes the Fourier transform in amere 145 fs. This is several orders of magnitude fasterthan devices based on silicon electronics are likely tobe able to achieve. This observation provokes an entic-ing proposition—the idea of high-speed, nondissipativelogic operations and algorithms would make for a rev-olution in physical instantiations of computational de-vices.

However, there are a number of important barriersthat will need to be overcome if such devices are to dis-place current high-speed electronics. First, the program-ming and readout of the device necessarily require sig-nificant resources, both in actual implementation and inprinciple. This overhead would need to be reduced dra-matically for such an approach to be feasible in prac-tice. Second, the connectivity required for implementinglarge-scale processors is missing. It is not yet possible tostring together a sequence of these Fourier transformerswith other operations in between in a way that enablesa real programmable device to be constructed. Third,this approach does not embrace the favorable scalingof the device that is the hallmark of quantum infor-mation processors. This is because the protocol makesuse of single-particle interference—a quantum effect tobe sure, but one which has analogs in classical wavephysics. The use of a molecular valence electron to con-trol and to readout the vibrational state means that theapproach lacks the multiparticle entanglement neededto realize exponential improvements on current compu-tational capacity. Recognizing the key element involvedas single-particle quantum interference raises the ques-tion as to whether a process based on wave interferencemight well be simulated entirely optically in an equallyefficient manner [6, 7].

Nonetheless, the notion of a classical processor with

DOI: 10.1103/Physics.3.38URL: http://link.aps.org/doi/10.1103/Physics.3.38

c© 2010 American Physical Society

Physics 3, 38 (2010)

such a dramatic speed-up suggests that it is worth con-tinuing to explore new ways to use physical systems toencode and manipulate information, and that this con-nection may reveal new insights into both physics andinto information processing.

References

[1] J. Ahn, T. C. Weinacht, and P. H. Bucksbaum, Science 287, 463(2000).

[2] M. N. Leuenberger and D. Loss, Nature 410, 789 (2001).[3] K. Hosaka, H. Shimada, H. Chiba, H. Katsuki, Y. Teranishi, Y. Oht-

suki, and K. Ohmori, Phys. Rev. Lett. 104, 180501 (2010).[4] T. Dunn, I. A. Walmsley, and S. Mukamel, Phys. Rev. Lett. 74, 884

(1995).[5] U. Leonhardt and M. G. Raymer, Phys. Rev. Lett. 76 1985 (1996).[6] E. Brainis et al., Phys. Rev. Lett. 90, 157902 (2003).[7] P. Londero, C. Dorrer, M. Anderson, S. Wallentowitz, K. Banaszek,

and I. A. Walmsley, Phys. Rev. A. 69, 0103029 (2004).

About the Author

Ian Walmsley

Ian Walmsley is the Hooke Professor of Experimental Physics at the University of Oxford,where he is also the Pro-Vice Chancellor for Research. He was formerly the Head of Atomicand Laser Physics at Oxford, and served as Director of the Institute of Optics at the Univer-sity of Rochester in the US. His research is in the area of optical science and engineering,and he is particularly interested in the applications of quantum optics to novel photonictechnologies, as well as the control of quantum systems. He has contributed particularly tothe development of methods for quantum tomography and in a different sphere to meth-ods for the complete characterization of ultrashort optical pulses, inventing the SPIDERtechnique. He is a fellow of the Optical Society of America, the American Physical Society,and the UK Institute of Physics, and leads a number of research collaborations, includingan EU Integrated Project on Qubit Applications. In 2008, Dr. Walmsley was named anOutstanding Referee by the American Physical Society.

DOI: 10.1103/Physics.3.38URL: http://link.aps.org/doi/10.1103/Physics.3.38

c© 2010 American Physical Society