Research


Molecular Quantum Control

Molecules are found in a diverse range of shapes and sizes, ranging from simple linear diatomics like hydrogen, oxygen and nitrogen, to complex organic or biological structures. Their resulting chemical and physical properties can depend strongly on the alignment or orientation of their internal structure with the outside environment. In the gas phase, a thermally-relaxed group of molecules will in general not be aligned or oriented with any particular axis in space, so that the effects of their internal structure cannot be isolated. A key challenge for scientists is then to find ways of preparing alignment or orientation of molecular samples in the laboratory frame. Given that molecules are bound by electrostatic forces, the simplest way to exert control is by applying an electric field.

An electric field distorts the charge distribution in a molecule, giving it a dipole moment. The molecule experiences a torque tending to align the dipole with the field.

An electric field distorts the charge distribution in a molecule, giving it a dipole moment. The molecule experiences a torque tending to align the dipole with the field.

When a quantum system is exposed to a static electric field, the shift in the system energy levels is known as the DC Stark effect. If the field strength is changed slowly, the levels will follow the field adiabatically. However, at higher frequencies the system cannot respond rapidly enough to follow the field; instead, they stabilize and follow the more slowly-varying intensity envelope of the field. This phenomenon is the non-resonant dynamic Stark effect (NRDSE), and is an extremely powerful way of controlling the rotational and vibrational dynamics of molecules. Careful application of shaped laser pulse sequences allows us to apply potentials designed to effect control of molecular dynamics using the NRDSE. For example, when a molecule is placed in a linearly-polarized laser field, even far from an absorption resonance, the field tends to polarize the molecule by distorting the electron distribution about its equilibrium position. Due to the internal molecular structure and its alignment relative to the field, the field-induced dipole will not generally be parallel to the field. As a result, the field will exert a torque on the molecule, tending to align its most polarizable axis with the field (see Figure). We have used the NRDSE to produce states of alignment (preferred axis in space) and orbital angular momentum orientation (preferred direction in space) in simple molecules using a variety of techniques[1-4].

Measured birefringence of CO2 during and after excitation using switched-wavepackets. At negative delays the sample is adiabatically aligned by a linearly-polarized 100ps pulse. When the pulse is rapidly truncated at zero-delay, the molecules are projected into a superposition of field-free states. Periodic revivals of the molecular wave-function cause field-free realignment of the sample, indicated by peaks in the birefringence.

Measured birefringence of CO2 during and after excitation using switched-wavepackets. At negative delays the sample is adiabatically aligned by a linearly-polarized 100ps pulse. When the pulse is rapidly truncated at zero-delay, the molecules are projected into a superposition of field-free states. Periodic revivals of the molecular wave-function cause field-free realignment of the sample, indicated by peaks in the birefringence.

One example is that of switched wavepackets [4], in which a 100ps “pump” pulse was shaped to have a relatively slow turn on (150ps) to its peak intensity, followed by a rapid truncation to zero intensity in only 200fs. When focussed into a sample of CO2 molecules, the molecules adiabatically align with the field via the NRDSE, before being released to rotate freely after the truncation of the field. Due to the coherence left in the sample after the pump pulse is turned off, the molecules subsequently realign during transient revivals. This can be seen in Figure 1, where the birefringence of the sample was measured as a function of delay relative to the pump pulse. The birefringence of the sample is a direct measure of the molecular alignment because the speed of light depends on its polarization relative to the molecular axis. During the adiabatic turn-on (negative delays) the birefringence of the sample gradually increases with the pump pulse intensity due to a combination of molecular alignment and distortion of the electron cloud by the pump pulse; after the field truncation (positive delays), transient peaks in the birefringence indicate revivals due to periodic rephasing of the molecular wavefunction.

Measured birefringence of CO2 during and after excitation using switched-wavepackets. At negative delays the sample is adiabatically aligned by a linearly-polarized 100ps pulse. When the pulse is rapidly truncated at zero-delay, the molecules are projected into a superposition of field-free states. Periodic revivals of the molecular wave-function cause field-free realignment of the sample, indicated by peaks in the birefringence.

Measured birefringence of CO2 during and after excitation using switched-wavepackets. At negative delays the sample is adiabatically aligned by a linearly-polarized 100ps pulse. When the pulse is rapidly truncated at zero-delay, the molecules are projected into a superposition of field-free states. Periodic revivals of the molecular wave-function cause field-free realignment of the sample, indicated by peaks in the birefringence.

In another example, when a short 50fs “pump” pulse is focussed into a sample of N2 molecules, it delivers a sharp alignment “kick” or torque to the sample, inducing coherence in the molecules as they start to rotate. In the frequency domain, this can be thought of as an impulsive Raman scattering transition where the pump pulse spectrum is broader than the rotational energy level splitting and so provides both the “pump” and “Stokes” frequencies necessary for a Raman transition. Figure 2 shows the measured birefringence of the sample as a function of delay relative to the pump: for positive delays, transient peaks in the birefringence indicate revivals due to the periodic rephasing of the molecular wavefunction.

Measured birefringence of CO2 during and after excitation using switched-wavepackets. At negative delays the sample is adiabatically aligned by a linearly-polarized 100ps pulse. When the pulse is rapidly truncated at zero-delay, the molecules are projected into a superposition of field-free states. Periodic revivals of the molecular wave-function cause field-free realignment of the sample, indicated by peaks in the birefringence.

Measured birefringence of CO2 during and after excitation using switched-wavepackets. At negative delays the sample is adiabatically aligned by a linearly-polarized 100ps pulse. When the pulse is rapidly truncated at zero-delay, the molecules are projected into a superposition of field-free states. Periodic revivals of the molecular wave-function cause field-free realignment of the sample, indicated by peaks in the birefringence.

In the final example of rotational control, we used a two-pulse sequence to demonstrate orbital angular momentum orientation in an H2 sample. In the first step, a 30fs “pump” pulse induced a weak rotational coherence in the sample by delivering a sharp “kick” to the sample, as in the previous example. A second, much longer and more powerful “amplification” pulse was then applied to the sample. As the amplification pulse drives the electron dynamics at its optical frequency ω, the slower rotational motion of the molecules modulates the dynamics at frequency Ω, causing the emission of a “Stokes” pulse at frequency (ω-Ω). As the Stokes pulse and amplification pulse propagate through the medium, energy is transferred from the amplification pulse to the Stokes pulse and to the molecules by stimulated Raman scattering so that the rotational coherence is enhanced/amplified by the interaction. This enhancement is shown in Figure 3, which shows the sample birefringence as a function of delay relative to the pump pulse. For the case of no amplification pulse (red plot) the birefringence decays due to collisions between the molecules. With the amplification pulse applied, the birefringence signal grows as a function of time from 75ps delay until it peaks at 150ps delay. In this example, the amplification pulse was circularly polarized so that it selectively enhanced specific coherences, introducing orbital angular momentum orientation to the sample.

1. Faraday Discussions, 153, 321-342, (2011) pdf
2. Physical Review A, 86, 053419 (2012) pdf
3. Physical Review Letters, 104, 193902 (2010)
4. Physical Review A, 73, 053403 (2006)