Quantum carpets from tumbling molecules


Molecules are comprised of charged particles whose spatial distribution is or could be distorted, lending the molecules a handle by which they can be manipulated via external electromagnetic fields.


Dr Burkhard Schmidt at the Freie Universität Berlin and Professor Bretislav Friedrich at the Fritz Haber Institute of the Max Planck Society in Berlin, along with colleagues, have been studying the effects of electromagnetic fields on molecular rotation and how these effects could be used to achieve quantum control.


Read the original article: https://doi.org/10.1080/00268976.2021.1966111


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Hello and welcome to Research Pod! Thank you for listening and joining us today.


In this episode, we’ll discuss how Dr Burkhard Schmidt at the Freie Universität Berlin, Professor Bretislav Friedrich at the Fritz Haber Institute of the Max Planck Society, and their research students Dr Marjan Mirahmadi and Mr Mallikarjun Karra are studying the effects of electromagnetic fields on molecular rotation and how these effects could be used to achieve quantum control.


The distribution of electrical charges in molecules is often non-uniform, making such molecules polar, which means endowed with what is called a permanent electric dipole moment. Even the charge distribution of non-polar molecules can be made non-uniform by action of a strong electromagnetic field such as that of a focused laser beam, which polarises the molecules and lends them an induced electric dipole moment. The dipole moments – permanent or induced – can then be used as handles by which the molecules can be manipulated via external electromagnetic fields. Such manipulation can be aimed either at controlling the rotation or the translation of the molecules – or both.


While the control of molecular translation encompasses deflection of molecular trajectories and confinement of molecules in traps, the control of molecular rotation entails molecular orientation and alignment. In this podcast, we will focus on the latter. Its applications range from reaction dynamics to Stark spectroscopy to high-order harmonic generation and orbital imaging to quantum computing and simulation.


The ability of electromagnetic fields to interact with the dipoles of molecules has been the focus of a research team in Berlin, Germany. Research leaders Dr Burkhard Schmidt and Professor Bretislav Friedrich, alongside Dr Marjan Mirahmadi and Mr Mallikarjun Karra, have been exploring how polar and polarisable rotors interact with electromagnetic fields in general and how the exact shape and duration of an electromagnetic pulse influence molecular rotation in particular.


The molecular systems Schmidt, Friedrich and colleagues have been focusing on are linear polar molecules, such as nitric oxide, known as NO, Carbonyl sulfide, known as OCS, and symmetric top molecules, such as ammonia, NH3, or iodomethane, CH3I. If such a molecule is left unperturbed, it rotates with a period given by factors such as the masses of the constituent atoms and their mutual distance. By applying an external electromagnetic field, it is possible to manipulate the rotation of the molecule.


Every molecule is polarisable but not every molecule is polar. The researchers examined what happens when a polar and polarisable molecule is acted upon not by many cycles of an electromagnetic wave, as is usually the case, but only by a half of one cycle. This is called a half-cycle pulse – or HCP for short. In such a case, the electric field of the HCP acts on both the permanent and induced electric dipole moments of the molecule. This gives rise to intriguing dynamics captured by the population quilts and quantum carpets. The electric field’s main effect is the creation of rotational wavepackets – combinations termed superpositions of rotor states whose composition changes periodically with time. It is a prerogative of quantum systems to exist in superpositions of different states, which amounts to being in different states at the same time. The quantum carpets reveal that after the passage of the pulse, the rotational wavepackets and the directional properties they encapsulate, namely orientation and alignment, undergo periodic revivals. This work is an important development in helping us understand what types of electromagnetic pulses are required to control the orientation and alignment of molecules. The team notes that orientation can be visualised by single-headed arrows whereas alignment is visualised by double-headed arrows.


In their study, the HCP was approximated either by a temporal delta pulse or by a temporal Gaussian pulse. While the former has no width – this is what ’delta’ means – the latter has a temporal width or length that can be varied. For the delta pulse, the researchers were able to solve the Schrödinger equation for the dynamics of the pulse’s interaction with the permanent and induced dipole moments of the molecule analytically. What is temporally long or short is determined by comparison with the rotational period of the molecule. The analytic solutions provided a rare insight into the dynamics of the rotational wavepackets that are created by an HCP.


For the Gaussian pulse, the problem is not analytically solvable, but can be solved numerically with high accuracy. The team’s numerical solution of the Schrödinger equation for the Gaussian pulse of very short duration, approximating a delta pulse, reproduced faithfully the analytic solutions they found for a delta pulse. For longer HCPs, the dynamics deviated from the ’delta-pulse dynamics’. In particular, they found that at certain pulse durations, the rotational energy and orientation imparted by the Gaussian pulse to the polar and polarisable rotor exhibits quasi-periodic drops. At first, they suspected numerical artifacts, but a thorough analysis revealed that the drops were real.


In a recent publication, the researchers provided a physical explanation for the quasi-periodic drops. In order to make the problem analytically tractable – and thereby their analysis insightful – they approximated the Gaussian pulse with a rectangular electric pulse. This analysis revealed that the drops result from the oscillating populations of rotational states that make up the wavepacket created by the pulse, and that they are necessarily accompanied by drops in the orientation and by a restoration of the pre-pulse alignment of the rotor. The ’oscillating populations’ arise due to rotational coherences, or phases, driven by the electric pulse whose probability is proportional to a sinc function of pulse duration. By making use of a simplified model comprised of just two rotational states for the interaction of the rectangular pulse with the rotor, the authors were able to recover the sinc probabilities and predict analytically at which pulse durations the sudden drops will occur. This previously unnoticed effect is an important one: by choosing the wrong pulse duration, the desired effect of the pulse – creation of a particular rotational wavepacket – will not and cannot be accomplished.


That’s all for this episode – thanks for listening, and stay subscribed to Research Pod for more of the latest science. See you again soon.

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