The motion of objects in free space is correlated because of the exchange of electromagnetic fields. These fields arise from the fluctuating charges in each object and also from external fluctuating fields, which polarize the objects and give rise to secondary fields. The fluctuating charges and fields are due to thermal and quantum zero-point fluctuations.

Dispersion forces, such as Casimir and Van der Waals forces, are conservative and dominated by quantum zero-point fluctuations and not by thermal fluctuations. However, an additional non-conservative force comes into play if the objects are in relative motion. Consequently, the motion of the objects slows down. This type of ’friction’ does not rely on mechanical contact between the objects and is therefore referred to as “vacuum friction”. The study of vacuum friction goes back to Einstein and Hopf, who were the first to calculate the damping coefficient acting on an atom in free space.

We study the friction experienced by a particle due to its interaction with thermal electromagnetic fields. The statistical correlation properties of thermal fields determine the strength of the particle’s dissipation. The statistical properties depend on the geometry of the particle’s environment as well as the electromagnetic properties of particle and surrounding matter. Our work is motivated by recent experiments that measured friction acting on nanoscale probes near planar substrates in ultra-high vacuum conditions. However, the physical picture underlying friction in nanoscale systems is still not clear. Our theory predicts that friction originates from electromagnetic interactions between dielectric objects as opposed to metallic objects. Furthermore, these interactions can penetrate through thin metal layers which explains previous discrepancies between theory and experiment.

The correlations between the two objects can be viewed in the weak and strong coupling regimes. In the latter, the two objects loose their identities and they become one entangled entity. We are interested in understanding this limit and its implications for experimental measurements. In the limit of strong coupling, the two objects mainly interact via evanescent waves, which can be expressed as “virtual photons”. Interestingly, evanescent waves are not orthogonal, and quantization can be accomplished only if the fields that generate the evanescent waves are also accounted for. Consequently, the quanta of evanescent fields are always connected to their sources and there are no purely evanescent photons in the plane-wave basis.

The two objects of interest in our work are referred to as probe and sample. On an elementary level, one can think of a near-field interaction between probe and sample as an electromagnetic interaction between a pair of two-level atoms - sample atom S and probe atom P. A question of central importance is, What is the probability for a system initially in a state |S=1, P=0; F=vac> (sample atom excited, probe atom in the ground state, and no external field, except for vacuum fluctuations) to change at some later time to the state |S=0, P=1; F=vac>? As pointed out by Power and Thirunamachandran, the problem leads to a noncausal result, which implies that it is not possible to know the initial and final states of both atoms. Indeed, one can infer a causal relationship between them only if the final states of sample and field are not specified, a result that has implications for near-field measurements. A measurement of the system alters the near-field and consequently captures information on the probe-sample interaction, not on the sample per se. This problem is rooted in so-called measurement back-action.

We are also interested in understanding how quantum correlations can be exploited in near-field measurements. For example, pairs of entangled photons can be used to increase the spatial resolution in near-field optical microscopy. We are developing experimental schemes to combine quantum imaging and near-field imaging.

Related Publications:

[1] D. Lopez-Mago and L. Novotny, ”Quantum-optical coherence tomography with collinear entangled photons,” Opt. Lett. 37, 4077-4079 (2012).

[2] D. Lopez-Mago and L. Novotny, ”Coherence measurements with the two-photonMichelson interferometer,” Phys. Rev. A 86, 023820 (2012).

[3] L. Novotny, ”Strong coupling, energy splitting, and level crossings: A classical perspective,” Am. J. Phys. 78, 1199-1202 (2010).

[4] L. Novotny and C. Henkel, ”Van der Waals versus optical interaction between metal nanoparticles,” Opt. Lett. 33, 1029-1031 (2008).

[5] J. R. Zurita-Sanchez, J.-J. Greffet, and L. Novotny, “Near-field friction due to fluctuating fields,” Phys. Rev. A 69, 02290 (2004).