Abstract
Topological operations can achieve certain goals without requiring accurate control over local operational details; for example, they have been used to control geometric phases and have been proposed as a way of controlling the state of certain systems within their degenerate subspaces1,2,3,4,5,6,7,8. More recently, it was predicted that topological operations can be used to transfer energy between normal modes, provided that the system possesses a specific type of degeneracy known as an exceptional point9,10,11. Here we demonstrate the transfer of energy between two vibrational modes of a cryogenic optomechanical device using topological operations. We show that this transfer arises from the presence of an exceptional point in the spectrum of the device. We also show that this transfer is non-reciprocal12,13,14. These results open up new directions in system control; they also open up the possibility of exploring other dynamical effects related to exceptional points15,16, including the behaviour of thermal and quantum fluctuations in their vicinity.
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Acknowledgements
We thank L. Jiang, D. Lee, T. Milburn, P. Rabl, S. Rotter, A. Shkarin and W. Underwood for discussions. This work was supported by AFOSR Grant FA9550-15-1-0270.
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H.X., D.M. and L.J. performed the measurements and analysed the data. J.G.E.H. and H.X. wrote the manuscript with input from all the authors. J.G.E.H. directed the research.
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Extended data figures and tables
Extended Data Figure 1 Experimental schematics.
a, Illustration of the optical and electronic components. The measurement laser (‘ML’) is split into a local oscillator (‘LO’ in b) and a probe beam (‘Probe’ in b). The probe-beam frequency is shifted by an acousto-optic modulator (‘AOM1’), and is locked to the cavity using a Pound–Drever–Hall (PDH) scheme and modulation produced by an electro-optic modulator (‘EOM’). The control laser (‘CL’; ‘Control’ in b) is locked to the measurement laser with a frequency offset that is approximately double the free spectral range of the cavity. The control parameters used to access the EP are the power P and detuning Δ of the control laser. P and Δ are set by the amplitude and frequency of a signal generator (‘SG’), which drives another acousto-optic modulator (‘AOM3’). The PDH error signal is used to control the frequency of yet another acousto-optic modulator (‘AOM2’), ensuring that all beams track fluctuations of the cavity. Light is delivered to (and collected from) the cryostat via an optical circulator. Coloured lines, hollow lines and thick black lines show free-space laser beams, optical fibres and electrical circuits, respectively. Triangles, ovals and semicircles show electronics, fibre couplers and photodiodes, respectively. ‘DAQ’ indicates the data acquisition system. The silicon nitride membrane is shown in purple. b, Illustration of the optical frequency domain. Lasers are indicated by coloured arrows and cavity modes by black curves.
Extended Data Figure 2 Lock-in signal at low laser power (Δ = −780 kHz, P = 73 μW).
Left, amplitude (top, red) and phase angle (bottom, blue) of the lock-in signal as a function of drive frequency. Right, the same data shown as a parametric plot of the in-phase and out-of-phase components of the lock-in signal as a function of drive frequency.
Extended Data Figure 3 Lock-in signal at high laser power (Δ = −780 kHz, P = 380 μW).
Left, amplitude (top, red) and phase angle (bottom, blue) of the lock-in signal as a function of drive frequency. Right, the same data shown as a parametric plot of the in-phase and out-of-phase components of the lock-in signal as a function of drive frequency.
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Xu, H., Mason, D., Jiang, L. et al. Topological energy transfer in an optomechanical system with exceptional points. Nature 537, 80–83 (2016). https://doi.org/10.1038/nature18604
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DOI: https://doi.org/10.1038/nature18604
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