2000 character limit reached
Quantum Optimal Control of Squeezing in Cavity Optomechanics (2405.19070v1)
Published 29 May 2024 in quant-ph and physics.optics
Abstract: Squeezing is a non-classical feature of quantum states that is a useful resource, for example in quantum sensing of mechanical forces. Here, we show how to use optimal control theory to maximize squeezing in an optomechanical setup with two external drives and determine how fast the mechanical mode can be squeezed. For the autonomous drives considered here, we find the inverse cavity decay to lower-bound the protocol duration. At and above this limit, we identify a family of protocols leveraging a two-stage control strategy, where the mechanical mode is cooled before it is squeezed. Identification of the control strategy allows for two important insights - to determine the factors that limit squeezing and to simplify the time-dependence of the external drives, making our protocol readily applicable in experiments.
- D. Walls and G. J. Milburn, eds., Quantum Optics (Springer Berlin Heidelberg, Berlin, Heidelberg, 2008).
- C. M. Caves, Quantum-mechanical noise in an interferometer, Phys. Rev. D 23, 1693 (1981).
- W. Qin, A. Miranowicz, and F. Nori, Beating the 3 db limit for intracavity squeezing and its application to nondemolition qubit readout, Phys. Rev. Lett. 129, 123602 (2022).
- M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity Optomechanics, Rev. Mod. Phys. 86, 1391 (2014).
- A. A. Clerk, Optomechanics and Quantum Measurement, in Quantum Optomechanics and Nanomechanics: Lecture Notes of the Les Houches Summer School: Volume 105, August 2015 (Oxford University Press, 2020) pp. 183–236.
- A. Kronwald, F. Marquardt, and A. A. Clerk, Arbitrarily large steady-state bosonic squeezing via dissipation, Phys. Rev. A 88, 063833 (2013).
- D. Basilewitsch, C. P. Koch, and D. M. Reich, Quantum Optimal Control for Mixed State Squeezing in Cavity Optomechanics, Adv. Quantum Technol. 2, 1800110 (2019).
- M. H. Goerz, T. Calarco, and C. P. Koch, The quantum speed limit of optimal controlled phasegates for trapped neutral atoms, 44, 154011 (2011), arXiv:1103.6050.
- K. Bhattacharyya, Quantum decay and the Mandelstam-Tamm time-energy inequality, Journal of Physics A: Mathematical and General 16, 2993 (1983).
- N. Margolus and L. B. Levitin, The maximum speed of dynamical evolution, Physica D: Nonlinear Phenomena 120, 188 (1998).
- L. B. Levitin and T. Toffoli, Fundamental Limit on the Rate of Quantum Dynamics: The Unified Bound Is Tight, Physical Review Letters 103, 160502 (2009).
- S. Deffner and S. Campbell, Quantum speed limits: from heisenberg’s uncertainty principle to optimal quantum control, Journal of Physics A: Mathematical and Theoretical 50, 453001 (2017).
- P. S. P. da Silva and P. Rouchon, Gate generation for open quantum systems via a monotonic algorithm with time optimization (2024), arXiv:2403.20028 [quant-ph] .
- C. K. Law, Interaction between a moving mirror and radiation pressure: A Hamiltonian formulation, Phys. Rev. A 51, 2537 (1995).
- H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford ; New York, 2002).
- V. F. Krotov, Global Methods in Optimal Control Theory, Monographs and Textbooks in Pure and Applied Mathematics No. 195 (M. Dekker, New York, 1996).
- A. I. Konnov and V. F. Krotov, On global methods for the successive improvement of control processes, Automation and Remote Control 60, 1427 (1999).
- J. P. Palao and R. Kosloff, Optimal control theory for unitary transformations, Phys. Rev. A 68, 062308 (2003).
- D. M. Reich, M. Ndong, and C. P. Koch, Monotonically convergent optimization in quantum control using Krotov’s method, The Journal of Chemical Physics 136, 104103 (2012).
- M. H. Goerz, D. M. Reich, and C. P. Koch, Optimal control theory for a unitary operation under dissipative evolution, New J. Phys. 16, 055012 (2014).
- M. H. Goerz, K. B. Whaley, and C. P. Koch, Hybrid optimization schemes for quantum control, EPJ Quantum Technol. 2, 21 (2015).
- J. P. Palao, R. Kosloff, and C. P. Koch, Protecting coherence in optimal control theory: State-dependent constraint approach, Phys. Rev. A 77, 063412 (2008).
- J. Yao, Photonic generation of microwave arbitrary waveforms, Optics Communications 284, 3723 (2011).
- G. Milburn and D. Walls, Production of squeezed states in a degenerate parametric amplifier, Optics Communications 39, 401 (1981).
- A. Mari and J. Eisert, Gently Modulating Optomechanical Systems, Phys. Rev. Lett. 103, 213603 (2009).
- J.-Q. Liao and C. K. Law, Parametric generation of quadrature squeezing of mirrors in cavity optomechanics, Phys. Rev. A 83, 033820 (2011).
- V. B. Braginsky, Y. I. Vorontsov, and K. S. Thorne, Quantum Nondemolition Measurements, Science 209, 547 (1980).
- R. Ruskov, K. Schwab, and A. N. Korotkov, Squeezing of a nanomechanical resonator by quantum nondemolition measurement and feedback, Phys. Rev. B 71, 235407 (2005).
- A. A. Clerk, F. Marquardt, and K. Jacobs, Back-action evasion and squeezing of a mechanical resonator using a cavity detector, New J. Phys. 10, 095010 (2008).
- A. Vinante and P. Falferi, Feedback-Enhanced Parametric Squeezing of Mechanical Motion, Phys. Rev. Lett. 111, 207203 (2013).
- P. Doria, T. Calarco, and S. Montangero, Optimal control technique for many-body quantum dynamics, Phys. Rev. Lett. 106, 190501 (2011).