Coherent control is a quantum mechanics-based method for controlling dynamical processes by light. The basic principle is to control quantum interference phenomena, typically by shaping the phase of laser pulses.[1][2] The basic ideas have proliferated, finding vast application in spectroscopy mass spectra, quantum information processing, laser cooling, ultracold physics and more.

Brief History

The initial idea was to control the outcome of chemical reactions. Two approaches were pursued:

in the time domain, a "pump-dump" scheme where the control is the time delay between pulses[3][4]
in the frequency domain, interfering pathways controlled by one and three photons.[5]

The two basic methods eventually merged with the introduction of optimal control theory.[6][7]

Experimental realizations soon followed in the time domain[8] and in the frequency domain.[9] Two interlinked developments accelerated the field of coherent control: experimentally, it was the development of pulse shaping by a spatial light modulator[10][11] and its employment in coherent control.[12] The second development was the idea of automatic feedback control[13] and its experimental realization.[14][15]

Coherent control aims to steer a quantum system from an initial state to a target state via an external field. For given initial and final (target) states, the coherent control is termed state-to-state control. A generalization is steering simultaneously an arbitrary set of initial pure states to an arbitrary set of final states i.e. controlling a unitary transformation. Such an application sets the foundation for a quantum gate operation.[16][17][18]

Controllability of a closed quantum system has been addressed by Tarn and Clark.[19] Their theorem based in control theory states that for a finite-dimensional, closed-quantum system, the system is completely controllable, i.e. an arbitrary unitary transformation of the system can be realized by an appropriate application of the controls[20] if the control operators and the unperturbed Hamiltonian generate the Lie algebra of all Hermitian operators. Complete controllability implies state-to-state controllability.

The computational task of finding a control field for a particular state-to-state transformation is difficult and becomes more difficult with the increase in the size of the system. This task is in the class of hard inversion problems of high computational complexity. The algorithmic task of finding the field that generates a unitary transformation scales factorial more difficult with the size of the system. This is because a larger number of state-to-state control fields have to be found without interfering with the other control fields.

Once constraints are imposed controllability can be degraded. For example, what is the minimum time required to achieve a control objective?[21] This is termed the "quantum speed limit".
Constructive approach to coherent control

The constructive approach uses a set of predetermined control fields for which the control outcome can be inferred.

The pump dump scheme [3][4] in the time domain and the three vs one photon interference scheme in the frequency domain [5] are prime examples. Another constructive approach is based on adiabatic ideas. The most well studied method is Stimulated raman adiabatic passage STIRAP [22] which employs an auxiliary state to achieve complete state-to-state population transfer.

One of the most prolific generic pulse shapes is a chirped pulse a pulse with a varying frequency in time.[23][24]
Optimal control

Optimal control as applied in coherent control seeks the optimal control field for steering a quantum system to its objective.[6][7] For state-to-state control the objective is defined as the maximum overlap at the final time T with the state \( {\displaystyle |\phi _{f}\rangle } \):

\( {\displaystyle J=|\langle \psi (T)|\phi _{f}\rangle |^{2}} \)

where the initial state is \( {\displaystyle |\phi _{i}\rangle } \). The time dependent control Hamiltonian has the typical form:

\( {\displaystyle H(t)=H_{0}+\mu \cdot \epsilon (t)}

where \( {\displaystyle \epsilon (t)} \) is the control field. Optimal control solves for the optimal field \( \epsilon (t) \) using the calculus of variations introducing Lagrange multipliers. A new objective functional is defined

\( {\displaystyle J'=J+\int _{0}^{T}\langle \chi (t)|\left(i{\frac {\partial }{\partial t}}-H(\epsilon (t))\right)|\psi (t)\rangle dt+\lambda \int _{o}^{T}|\epsilon (t)|^{2}dt} \)

where \( {\displaystyle |\chi \rangle } \) is a wave function like Lagrange multiplier and the λ {\displaystyle \lambda } \lambda parameter regulates the integral intensity. Variation of \( {\displaystyle J'} \) with respect to \( {\displaystyle \delta \epsilon } \) and \( {\displaystyle \delta \psi } \) leads to two coupled Schrödinger equations. A forward equation for \( |\psi \rangle \) with initial condition \( {\displaystyle |\psi (0)\rangle =|\phi _{i}\rangle } \) and a backward equation for the Lagrange multiplier \( {\displaystyle |\chi \rangle } \) with final condition \( {\displaystyle |\chi (T)\rangle =|\phi _{f}\rangle } \). Finding a solution requires an iterative approach. Different algorithms have been applied for obtaining the control field such as the Krotov method.[25]

A local in time alternative method has been developed,[26] where at each time step, the field is calculated to direct the state to the target. A related method has been called tracking [27]
Experimental applications

Some applications of coherent control are

Unimolecular and bimolecular chemical reactions.[28][29][30]
The biological photoisomerization of Retinal.[31][32]
The field of nuclear magnetic resonance.[33]
The field of ultracold matter for photoassociation.[34]
Laser cooling of internal degrees of freedom.[35][36]
Quantum information processing.[37][38][39]
Attosecond physics.[40][41]

Another important issue is the spectral selectivity of two photon coherent control.[42] These concepts can be applied to single pulse Raman spectroscopy and microscopy.[43]

As one of the cornerstones for enabling quantum technologies, optimal quantum control keeps evolving and expanding into areas as diverse as quantum-enhanced sensing, manipulation of single spins, photons, or atoms, optical spectroscopy, photochemistry, magnetic resonance (spectroscopy as well as medical imaging), quantum information processing, and quantum simulation.[44]

Gordon, Robert J.; Rice, Stuart A. (1997). "Active control of the dynamics of atoms and molecules". Annual Review of Physical Chemistry. 48 (1): 601–641. Bibcode:1997ARPC...48..601G. doi:10.1146/annurev.physchem.48.1.601. ISSN 0066-426X. PMID 15012451.
Shapiro, Moshe; Brumer, Paul (2000). "Coherent Control of Atomic, Molecular, and Electronic Processes". Advances in Atomic, Molecular and Optical Physics. 42. Academic Press. pp. 287–345. doi:10.1016/s1049-250x(08)60189-5. ISBN 978-0-12-003842-8. ISSN 1049-250X.
Tannor, David J.; Rice, Stuart A. (1985-11-15). "Control of selectivity of chemical reaction via control of wave packet evolution". The Journal of Chemical Physics. 83 (10): 5013–5018. doi:10.1063/1.449767. ISSN 0021-9606.
Tannor, David J.; Kosloff, Ronnie; Rice, Stuart A. (1986-11-15). "Coherent pulse sequence induced control of selectivity of reactions: Exact quantum mechanical calculations". The Journal of Chemical Physics. 85 (10): 5805–5820. doi:10.1063/1.451542. ISSN 0021-9606.
Brumer, Paul; Shapiro, Moshe (1986). "Control of unimolecular reactions using coherent light". Chemical Physics Letters. 126 (6): 541–546. doi:10.1016/s0009-2614(86)80171-3. ISSN 0009-2614.
Peirce, Anthony P.; Dahleh, Mohammed A.; Rabitz, Herschel (1988-06-01). "Optimal control of quantum-mechanical systems: Existence, numerical approximation, and applications". Physical Review A. 37 (12): 4950–4964. doi:10.1103/physreva.37.4950. ISSN 0556-2791. PMID 9899641.
Kosloff, R.; Rice, S.A.; Gaspard, P.; Tersigni, S.; Tannor, D.J. (1989). "Wavepacket dancing: Achieving chemical selectivity by shaping light pulses". Chemical Physics. 139 (1): 201–220. doi:10.1016/0301-0104(89)90012-8. ISSN 0301-0104.
Baumert, T.; Engel, V.; Meier, C.; Gerber, G. (1992). "High laser field effects in multiphoton ionization of Na2. Experiment and quantum calculations". Chemical Physics Letters. 200 (5): 488–494. doi:10.1016/0009-2614(92)80080-u. ISSN 0009-2614.
Zhu, L.; Kleiman, V.; Li, X.; Lu, S. P.; Trentelman, K.; Gordon, R. J. (1995-10-06). "Coherent Laser Control of the Product Distribution Obtained in the Photoexcitation of HI". Science. 270 (5233): 77–80. doi:10.1126/science.270.5233.77. ISSN 0036-8075. S2CID 98705974.
Weiner, A. M. (2000). "Femtosecond pulse shaping using spatial light modulators" (PDF). Review of Scientific Instruments. 71 (5): 1929–1960. doi:10.1063/1.1150614. ISSN 0034-6748. Archived (PDF) from the original on 17 April 2007. Retrieved 2010-07-06.
Liquid Crystal Optically Addressed Spatial Light Modulator, [1] Archived 2012-02-04 at the Wayback Machine

Slinger, C.; Cameron, C.; Stanley, M.; "Computer-Generated Holography as a Generic Display Technology" Archived 2011-09-27 at the Wayback Machine, IEEE Computer, Volume 38, Issue 8, Aug. 2005, pp 46–53

Kawashima, Hitoshi; Wefers, Marc M.; Nelson, Keith A. (1995). "Femtosecond Pulse Shaping, Multiple-Pulse Spectroscopy, and Optical Control". Annual Review of Physical Chemistry. 46 (1): 627–656. doi:10.1146/annurev.pc.46.100195.003211. ISSN 0066-426X. PMID 24341370.
Judson, Richard S.; Rabitz, Herschel (1992-03-09). "Teaching lasers to control molecules". Physical Review Letters. 68 (10): 1500–1503. doi:10.1103/physrevlett.68.1500. ISSN 0031-9007. PMID 10045147.
Assion, A. (1998-10-30). "Control of Chemical Reactions by Feedback-Optimized Phase-Shaped Femtosecond Laser Pulses". Science. 282 (5390): 919–922. doi:10.1126/science.282.5390.919. PMID 9794756.
Brif, Constantin; Chakrabarti, Raj; Rabitz, Herschel (2010-07-08). "Control of quantum phenomena: past, present and future". New Journal of Physics. 12 (7): 075008. doi:10.1088/1367-2630/12/7/075008. ISSN 1367-2630.
Tesch, Carmen M.; Kurtz, Lukas; de Vivie-Riedle, Regina (2001). "Applying optimal control theory for elements of quantum computation in molecular systems". Chemical Physics Letters. 343 (5–6): 633–641. doi:10.1016/s0009-2614(01)00748-5. ISSN 0009-2614.
Palao, José P.; Kosloff, Ronnie (2002-10-14). "Quantum Computing by an Optimal Control Algorithm for Unitary Transformations". Physical Review Letters. 89 (18): 188301.arXiv:quant-ph/0204101. doi:10.1103/physrevlett.89.188301. ISSN 0031-9007. PMID 12398642. S2CID 9237548.
Rabitz, Herschel; Hsieh, Michael; Rosenthal, Carey (2005-11-30). "Landscape for optimal control of quantum-mechanical unitary transformations". Physical Review A. 72 (5): 052337. doi:10.1103/physreva.72.052337. ISSN 1050-2947.
Huang, Garng M.; Tarn, T. J.; Clark, John W. (1983). "On the controllability of quantum‐mechanical systems". Journal of Mathematical Physics. 24 (11): 2608–2618. doi:10.1063/1.525634. ISSN 0022-2488.
Ramakrishna, Viswanath; Salapaka, Murti V.; Dahleh, Mohammed; Rabitz, Herschel; Peirce, Anthony (1995-02-01). "Controllability of molecular systems". Physical Review A. 51 (2): 960–966. doi:10.1103/physreva.51.960. ISSN 1050-2947. PMID 9911672.
Caneva, T.; Murphy, M.; Calarco, T.; Fazio, R.; Montangero, S.; Giovannetti, V.; Santoro, G. E. (2009-12-07). "Optimal Control at the Quantum Speed Limit". Physical Review Letters. 103 (24): 240501.arXiv:0902.4193. doi:10.1103/physrevlett.103.240501. ISSN 0031-9007. PMID 20366188. S2CID 43509791.
Unanyan, R.; Fleischhauer, M.; Shore, B.W.; Bergmann, K. (1998). "Robust creation and phase-sensitive probing of superposition states via stimulated Raman adiabatic passage (STIRAP) with degenerate dark states". Optics Communications. 155 (1–3): 144–154. doi:10.1016/s0030-4018(98)00358-7. ISSN 0030-4018.
Ruhman, S.; Kosloff, R. (1990-08-01). "Application of chirped ultrashort pulses for generating large-amplitude ground-state vibrational coherence: a computer simulation". Journal of the Optical Society of America B. 7 (8): 1748–1752. doi:10.1364/josab.7.001748. ISSN 0740-3224.
Cerullo, G.; Bardeen, C.J.; Wang, Q.; Shank, C.V. (1996). "High-power femtosecond chirped pulse excitation of molecules in solution". Chemical Physics Letters. 262 (3–4): 362–368. doi:10.1016/0009-2614(96)01092-5. ISSN 0009-2614.
Somlói, József; Kazakov, Vladimir A.; Tannor, David J. (1993). "Controlled dissociation of I2 via optical transitions between the X and B electronic states". Chemical Physics. 172 (1): 85–98. doi:10.1016/0301-0104(93)80108-l. ISSN 0301-0104.
Kosloff, Ronnie; Hammerich, Audrey Dell; Tannor, David (1992-10-12). "Excitation without demolition: Radiative excitation of ground-surface vibration by impulsive stimulated Raman scattering with damage control". Physical Review Letters. 69 (15): 2172–2175. doi:10.1103/physrevlett.69.2172. ISSN 0031-9007. PMID 10046417.
Chen, Yu; Gross, Peter; Ramakrishna, Viswanath; Rabitz, Herschel; Mease, Kenneth (1995-05-22). "Competitive tracking of molecular objectives described by quantum mechanics". The Journal of Chemical Physics. 102 (20): 8001–8010. doi:10.1063/1.468998. ISSN 0021-9606.
Levis, R. J.; Rabitz, H. A. (2002). "Closing the Loop on Bond Selective Chemistry Using Tailored Strong Field Laser Pulses". The Journal of Physical Chemistry A. 106 (27): 6427–6444. doi:10.1021/jp0134906. ISSN 1089-5639.
Dantus, Marcos; Lozovoy, Vadim V. (2004). "Experimental Coherent Laser Control of Physicochemical Processes". Chemical Reviews. 104 (4): 1813–1860. doi:10.1021/cr020668r. ISSN 0009-2665. PMID 15080713.
Levin, Liat; Skomorowski, Wojciech; Rybak, Leonid; Kosloff, Ronnie; Koch, Christiane P.; Amitay, Zohar (2015-06-10). "Coherent Control of Bond Making". Physical Review Letters. 114 (23): 233003.arXiv:1411.1542. doi:10.1103/physrevlett.114.233003. ISSN 0031-9007. PMID 26196798. S2CID 32145743.
Prokhorenko, V. I. (2006-09-01). "Coherent Control of Retinal Isomerization in Bacteriorhodopsin". Science. 313 (5791): 1257–1261. doi:10.1126/science.1130747. ISSN 0036-8075. PMID 16946063. S2CID 8804783.
Wohlleben, Wendel; Buckup, Tiago; Herek, Jennifer L.; Motzkus, Marcus (2005-05-13). "Coherent Control for Spectroscopy and Manipulation of Biological Dynamics". ChemPhysChem. 6 (5): 850–857. doi:10.1002/cphc.200400414. ISSN 1439-4235. PMID 15884067.
Khaneja, Navin; Reiss, Timo; Kehlet, Cindie; Schulte-Herbrüggen, Thomas; Glaser, Steffen J. (2005). "Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms". Journal of Magnetic Resonance. 172 (2): 296–305. doi:10.1016/j.jmr.2004.11.004. ISSN 1090-7807. PMID 15649756.
Wright, M. J.; Gensemer, S. D.; Vala, J.; Kosloff, R.; Gould, P. L. (2005-08-01). "Control of Ultracold Collisions with Frequency-Chirped Light" (PDF). Physical Review Letters. 95 (6): 063001. doi:10.1103/physrevlett.95.063001. ISSN 0031-9007. PMID 16090943.
Viteau, M.; Chotia, A.; Allegrini, M.; Bouloufa, N.; Dulieu, O.; Comparat, D.; Pillet, P. (2008-07-11). "Optical Pumping and Vibrational Cooling of Molecules". Science. 321 (5886): 232–234.arXiv:0806.3829. doi:10.1126/science.1159496. ISSN 0036-8075. PMID 18621665. S2CID 13059237.
Lien, Chien-Yu; Seck, Christopher M; Lin, Yen-Wei; Nguyen, Jason H.V.; Tabor, David A.; Odom, Brian C. (2014-09-02). "Broadband optical cooling of molecular rotors from room temperature to the ground state". Nature Communications. 5 (1): 4783.arXiv:1402.3918. doi:10.1038/ncomms5783. ISSN 2041-1723. PMID 25179449.
García-Ripoll, J. J.; Zoller, P.; Cirac, J. I. (2003-10-07). "Speed Optimized Two-Qubit Gates with Laser Coherent Control Techniques for Ion Trap Quantum Computing". Physical Review Letters. 91 (15): 157901.arXiv:quant-ph/0306006. doi:10.1103/physrevlett.91.157901. ISSN 0031-9007. PMID 14611499.
Larsen, T. W., K. D. Petersson, F. Kuemmeth, T. S. Jespersen, P. Krogstrup, and C. M. Marcus. "Coherent control of a transmon qubit with a nanowire-based Josephson junction." Bulletin of the American Physical Society 60 (2015).
Scharfenberger, Burkhard; Munro, William J; Nemoto, Kae (2014-09-25). "Coherent control of an NV− center with one adjacent 13C". New Journal of Physics. 16 (9): 093043.arXiv:1404.0475. doi:10.1088/1367-2630/16/9/093043. ISSN 1367-2630.
Corkum, P. B.; Krausz, Ferenc (2007). "Attosecond science". Nature Physics. Springer Science and Business Media LLC. 3 (6): 381–387. doi:10.1038/nphys620. ISSN 1745-2473.
Boutu, W.; Haessler, S.; Merdji, H.; Breger, P.; Waters, G.; et al. (2008-05-04). "Coherent control of attosecond emission from aligned molecules". Nature Physics. Springer Science and Business Media LLC. 4 (7): 545–549. doi:10.1038/nphys964. hdl:10044/1/12527. ISSN 1745-2473.
Meshulach, Doron; Silberberg, Yaron (1998). "Coherent quantum control of two-photon transitions by a femtosecond laser pulse". Nature. Springer Science and Business Media LLC. 396 (6708): 239–242. doi:10.1038/24329. ISSN 0028-0836. S2CID 41953962.
Silberberg, Yaron (2009). "Quantum Coherent Control for Nonlinear Spectroscopy and Microscopy". Annual Review of Physical Chemistry. 60 (1): 277–292. doi:10.1146/annurev.physchem.040808.090427. ISSN 0066-426X. PMID 18999997.

Glaser, Steffen J.; Boscain, Ugo; Calarco, Tommaso; Koch, Christiane P.; Köckenberger, Walter; et al. (2015). "Training Schrödinger's cat: quantum optimal control". The European Physical Journal D. 69 (12): 1–24.arXiv:1508.00442. doi:10.1140/epjd/e2015-60464-1. ISSN 1434-6060.

Further reading

Principles of the Quantum Control of Molecular Processes, by Moshe Shapiro, Paul Brumer, pp. 250. ISBN 0-471-24184-9. Wiley-VCH, (2003).
"Quantum control of Molecular Processes", Moshe Shapiro and Paul Brumer, Wiley-VCH (2012).
Rice, Stuart Alan, and Meishan Zhao. Optical control of molecular dynamics. New York: John Wiley, 2000.
d'Alessandro, Domenico. Introduction to quantum control and dynamics. CRC press, 2007.
David J. Tannor, "Introduction to Quantum Mechanics: A Time-dependent Perspective", (University Science Books, Sausalito, 2007).

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