Quantum Coherent Conrol

 

Quantum Coherent Control

It is control that turns scientific knowledge into technology. The general goal of quantum control is to manipulate dynamical processes at the atomic or molecular scale, typically using external electromagnetic field. The objective of quantum optimal control is to devise and implement shapes of pulses of external field or sequences of such pulses, that accomplish a given task in a quantum system in the best possible manner.

The challenge of manipulating nature at the quantum level has a huge potential for current and future applications. Quantum optimal control is a part of the effort to engineer quantum technologies from the bottom up. Currently the emerging quantum technologies are based on superposition, entanglement and many-body quantum states. Quantum control is thus a strategic cross-sectional field of research, enabling and leveraging current and future quantum technology applications.

The field of quantum control has been initiated by the idea of controlling chemical reactions [1–5]. It was soon realised that the principles of quantum control through interfering pathways is universal and spread to other fields such as quantum information [6,7]. A recent overview has been published which emphasises the future prospects of the field [8]. Coherent control can be applied directly to controlling matter waves using a BEC as a source of matter waves. We have pioneered this idea.

Despite the success and proliferation of coherent control the dream of controlling chemical reactions has not been achieved. To fill this gap our recent efforts concentrated on control of binary reactions. As a first step in coherent control of binary-chemical reactions we studied both experimentally and theoretically the photoassociation of hot Mg2[9]. We were able to identify two mechanisms of coherent control. The first is based on multiphoton interference pathways. The second is vibrationally assisted [10]. The pulse shaping was carried out by a spatial light modulator in the frequency domain. The other extreme case is coherent control of photoassociation of ultracold Rb2[11]. The duration of the control pulse is four orders of magnitude longer than the pulse used for Mg2 photoassociation. For the Rb2 case the pulse shaping was carried out in the time domain. In both the photoassociation of the Mg2 and the Rb2 the reaction leads to a significant reduction of translational entropy. The next step in control of binary reactions should be devoted to processes of the type AB + C → A + BC → AC + B. This will require a combined experimental and theoretical effort.

Photoassociation of hot Mg2

A natural meeting point between Quantum thermodynamics and coherent control is to develop method to cool internal degrees of freedom of molecules [12]. We originated this quest of cooling internal degrees of freedom of molecules by broad band excitations [13–14]. This scheme has been realised experimentally in broad band cooling the vibrations of Cs2 [15–18] and rotational cooling of trapped molecular ions [19]. The current challenge is a simultaneous cooling of both vibrational and rotational degrees of freedom [20]. The difficulty emerges from the large separation of time scales.

The coherent control required to achieve these tasks is of an open quantum system. It would seem that decoherence in open systems will destroy the interference required to generated control. Nevertheless in some cases the the environment allows control which otherwise could not be achieved [21, 22]. An outstanding issue is coherent control in weak field. For isolated systems for target operators that commute with the system hamiltonian phase only coherent control is impossible [23]. We were able to extend this theorem of no phase control to Markovian evolution of open systems [24]. Nevertheless there is unpublished experimental data indicating asymmetry between positive and negative chirp in weak field absorption. If verified, it would indicate to an experimental procedure to unravel non-Markovian dynamics.

The issue of controllability has not been resolved. What can be controlled by interference? What is the minimal time to achieve such a control? What is the optimal control protocol? These issues deserve further study in the context of open quantum systems. An important issue is the influence of noise. In particular the unavoidable noise on the controller. Such noise is fast relative to the timescale of the controlled system. Can one circumvent the influence of this noise by cooling the system? In the context of quantum information this is known as adding an ancilla qubit.

Coherent Control has become an essential component in achieving quantum gates [6]. What is unique is the requirement of extremely high fidelity. A related issue is how to obtain a quantum gate under noisy conditions [7]. The same type of gates for example swap gates can be used for quantum heat engines.

All practical engines require active control to achieve their goals. Quantum heat engines are no exception, they require monitoring and feedback. But in quantum mechanics constant monitoring can change the state of the working medium, for example measuring energy will destroy coherence. We only started to tackle this issue [27] which is related to quantum measurement and control [25].

Active quantum control requires measurement and feedback [27]. This issue has not been studied in a thermodynamical context. Quantum thermodynamics and quantum control are natural mates. Quantum control is the enabler of the coherent manipulations required in a truly quantum heat device. Advance in one field has immediate consequence in the other.

References

[1] Paul Brumer and Moshe Shapiro. Control of unimolecular reactions using coherent light. Chemical physics letters, 126(6):541–546, 1986.
[2] Moshe Shapiro and Paul Brumer. Coherent control of atomic, molecular, and electronic processes. Advances in atomic, molecular, and optical physics, 42:287–345, 2000.
[3] David J Tannor and Stuart A Rice. Control of selectivity of chemical reaction via control of wave packet evolution. The Journal of chemical physics, 83(10):5013–5018, 1985.
[4] David J Tannor, Ronnie Kosloff, and Stuart A Rice. Coherent pulse sequence induced control of selectivity of reactions: Exact quantum mechanical calculations. The Journal of Chemical Physics, 85(10):5805–5820, 1986.
[5] Ronnie Kosloff, Stuart A Rice, Pier Gaspard, Sam Tersigni, and DJ Tannor. Wavepacket dancing: Achieving chemical selectivity by shaping light pulses. Chemical Physics, 139(1): 201–220, 1989.
[6] Jos´e P Palao and Ronnie Kosloff. Quantum computing by an optimal control algorithm for unitary transformations. Physical Review Letters, 89(18):188301, 2002.
[7] Daniel M Reich, Nadav Katz, and Christiane P Koch. Exploiting non-markovianity for quantum control. Scientific reports, 5, 2015.
[8] Steffen J. Glaser, Ugo Boscain, Tommaso Calarco, Christiane P. Koch, Walter Kckenberger,Ronnie Kosloff, Ilya Kuprov, Burkhard Luy, Sophie Schirmer, Thomas Schulte- Herbrggen,Dominique Sugny, and Frank K. Wilhelm. Training schro¨dingers cat: quantum optimal control. The European Physical Journal D, 69(12), 2015.
[9] Liat Levin, Wojciech Skomorowski, Leonid Rybak, Ronnie Kosloff, Christiane P Koch, and Zohar Amitay. Coherent control of bond making. Physical Review Letters, 114(2):233003,2015.
[10] Liat Levin, Wojciech Skomorowski, Ronnie Kosloff, Christiane Koch, and Zohar Amitay. The performance of rationally phase-shaped femtosecond laser pulses. Journal of Physics B: Atomic Molecular and Optical Physics, 48(18):184004, 2015.
[11] JL Carini, S Kallush, R Kosloff, and PL Gould. Enhancement of ultracold molecule formation using shaped nanosecond frequency chirps. Phys. Rev. Lett., 115:173003, 2015.
[12] Martin Zeppenfeld, Barbara GU Englert, Rosa Glo¨ckner, Alexander Prehn, Manuel Mielenz, Christian Sommer, Laurens D van Buuren, Michael Motsch, and Gerhard Rempe. Sisyphus cooling of electrically trapped polyatomic molecules. Nature, 491(7425):570–573, 2012.
[13] Allon Bartana, Ronnie Kosloff, and David J Tannor. Laser cooling of molecular internal degrees of freedom by a series of shaped pulses. The Journal of Chemical Physics, 99(1):196–210, 1993.
[14] Allon Bartana, Ronnie Kosloff, and David J Tannor. Laser cooling of internal degrees of freedom. ii. The Journal of Chemical Physics, 106(4):1435–1448, 1997.
[15] Allon Bartana, Ronnie Kosloff, and David J Tannor. Laser cooling of molecules by dynamically trapped states. Chemical Physics, 267(1):195–207, 2001.
[16] Matthieu Viteau, Amodsen Chotia, Maria Allegrini, Nadia Bouloufa, Olivier Dulieu, Daniel Comparat, and Pierre Pillet. Optical pumping and vibrational cooling of molecules. Science, 321(5886):232–234, 2008.
[17] Dimitris Sofikitis, S´ebastien Weber, Andr´ea Fioretti, Ridha Horchani, Maria Allegrini, B´eatrice Chatel, Daniel Comparat, and Pierre Pillet. Molecular vibrational cooling by optical pumping with shaped femtosecond pulses. New Journal of Physics, 11(5):055037, 2009.
[18] Olivier Dulieu and Carlo Gabbanini. The formation and interactions of cold and ultracold molecules: new challenges for interdisciplinary physics. Reports on progress in physics, 72(8):086401, 2009.
[19] Chien-Yu Lien, Christopher M Seck, Yen-Wei Lin, Jason HV Nguyen, David A Tabor, and Brian C Odom. Broadband optical cooling of molecular rotors from room temperature to the ground state. Nature communications, 5, 2014.
[20] Daniel Comparat. Molecular cooling via sisyphus processes. Physical Review A, 89(4): 043410, 2014.
[21] Rebing Wu, Alexander Pechen, Herschel Rabitz, Michael Hsieh, and Benjamin Tsou. Control landscapes for observable preparation with open quantum systems. Journal of Mathematical Physics, 49(2):022108, 2008.
[22] Christiane P Koch. Controlling open quantum systems: tools, achievements, and limitations. Journal of Physics: Condensed Matter, 28(21):213001, 2016.
[23] Leonardo A Pacho´n, Li Yu, and Paul Brumer. Coherent one-photon phase control in closed and open quantum systems: A general master equation approach. Faraday discussions, 163:485– 495, 2013.
[24] Morag Am-Shallem and Ronnie Kosloff. The scaling of weak field phase-only control in markovian dynamics. The Journal of Chemical Physics, 141(4):044121, 2014.
[25] Howard M Wiseman and Gerard J Milburn. Quantum measurement and control. Cambridge University Press, 2009.
[27] Amikam Levy, Lajos Diosi, and Ronnie Kosloff, Quantum Flywheel, Phys. Rev. A 93, 052119 (2016).