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Doppler cooling is a widely used technique to laser cool atoms and nanoparticles exploiting the Doppler shift involved in translational transformations. The rotational Doppler effect arising from rotational coordinate transformations should similarly enable optical manipulations of the rotational degrees of freedom in rotating nanosystems. Here, we show that rotational Doppler cooling and heating (RDC and RDH) effects embody rich and unexplored physics, such as a strong dependence on particle morphology. For geometrically confined particles, such as a nanorod that can represent diatomic molecules, RDC and RDH follow similar rules as their translational Doppler counterpart, where cooling and heating are always observed at red- or blue-detuned laser frequencies, respectively. Surprisingly, nanosystems that can be modeled as a solid particle shows a strikingly different response, where RDH appears in a frequency regime close to their resonances, while a detuned frequency produces cooling of rotation. We also predict that the RDH effect can lead to unprecedented spontaneous chiral symmetry breaking, whereby an achiral particle under linearly polarized illumination starts spontaneously rotating, rendering it nontrivial compared to the translational Doppler effect. Our results open up new exciting possibilities to control the rotational motion of molecules and nanoparticles.
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A monochromatic linear source of light is rotated with certain angular frequency and when such light is analysed after reflection then a change of frequency or wavelength may be observed depending on the location of the observer. This change of frequency or wavelength is different from the classical Doppler effect [1] or relativistic Doppler effect [2]. The reason behind this shift in wavelength is that a certain time interval observed by an observer in the rotating frame is different from that of a stationary observer.
We propose and substantiate experimentally the cascaded rotational Doppler effect for interactions of spinning objects with light carrying angular momentum. Based on the law of parity conservation for electromagnetic interactions, we reveal that the frequency shift can be doubled through cascading two rotational Doppler processes which are mirror-imaged to each other. This effect is further experimentally verified with a rotating half-wave plate, and the mirror-imaging process is achieved by reflecting the frequency-shifted circularly polarized wave upon a mirror with a quarter-wave plate in front of it. The mirror symmetry and thus parity conservation guarantees that this doubled frequency shift can be further multiplied with more successive mirror-imaging conjugations, with photons carrying spin and/or orbital angular momentum, which could be widely applied for detection of rotating systems ranging from molecules to celestial bodies with high precision and sensitivity.
The frequency shift of a helical light beam experiencing the rotation near the axis deferring from its own axis (conical evolution) is studied theoretically. Both the energy and the kinematic approaches lead to a paradoxical conclusion that after a whole cycle of the system rotation the beam does not return to its initial state. Another paradox is manifested in the peculiar behavior of the beam transverse pattern rotation at different geometric parameters of the evolving system. A fundamental role of the detecting system motion is substantiated. The special natural observers motion is found for which both paradoxes are eliminated. Relations of the described facts with the Hannays geometric phase concept are discussed.
Linearly polarized light can exert a torque on a birefringent object when passing through it. This phenomena, present in Maxwells equations, was revealed by Poynting and beautifully demonstrated in the pioneer experiments of Beth and Holbourn. Modern uses of this effect lie at the heart of optomechanics with angular momentum exchange between light and matter. A milestone of controlling movable massive objects with light is the reduction of their mechanical fluctuations, namely cooling. Optomechanical cooling has been implemented through linear momentum transfer of the electromagnetic field in a variety of systems, but remains unseen for angular momentum transfer to rotating objects. We present the first observation of cooling in a rotational optomechanical system. Particularly, we reduce the thermal noise of the torsional modes of a birefringent optical nanofiber, with resonant frequencies near 200 kHz and a Q-factor above $mathbf{2times10^4}$. Nanofibers are centimeter long, sub-micrometer diameter optical fibers that confine propagating light, reaching extremely large intensities, hence enhancing optomechanical effects. The nanofiber is driven by a propagating linearly polarized laser beam. We use polarimetry of a weak optical probe propagating through the nanofiber as a proxy to measure the torsional response of the system. Depending on the polarization of the drive, we can observe both reduction and enhancement of the thermal noise of many torsional modes, with noise reductions beyond a factor of two. The observed effect opens a door to manipulate the torsional motion of suspended optical waveguides in general, expanding the field of rotational optomechanics, and possibly exploiting its quantum nature for precision measurements in mesoscopic systems.
The function to measure orbital angular momentum (OAM) distribution of vortex light is essential for OAM applications. Although there are lots of works to measure OAM modes, it is difficult to measure the power distribution of different OAM modes quantitatively and instantaneously, let alone measure the phase distribution among them. In this work, we demonstrate an OAM complex spectrum analyzer, which enables to measure the power and phase distribution of OAM modes simultaneously by employing rotational Doppler Effect. The original OAM mode distribution is mapped to electrical spectrum of beating signals with a photodetector. The power distribution and phase distribution of superimposed OAM beams are successfully retrieved by analyzing the electrical spectrum. We also extend the measurement to other spatial modes, such as linear polarization modes. These results represent a new landmark of spatial mode analysis and show great potentials in optical communication and OAM quantum state tomography.
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