Continuous-time quantum harmonic oscillator state engineering
arXiv:2304.08351 · doi:10.1088/1367-2630/ad149c
Abstract
The center of mass motion of trapped ions and neutral atoms is suitable for approximation by a time-dependent driven quantum harmonic oscillator whose frequency and driving strength may be controlled with high precision. We show the time evolution for these systems with continuous differentiable time-dependent parameters in terms of the three basic operations provided by its underlying symmetry, rotation, displacement, and squeezing, using a Lie algebraic approach. Our factorization of the dynamics allows for the intuitive construction of protocols for state engineering, for example, creating and removing displacement and squeezing, as well as their combinations, optimizing squeezing, or more complex protocols that work for slow and fast rates of change in the oscillator parameters.
arXiv comment19 pages, 9 figures
References in corpus (16)
- Gaussian Quantum Information
- Quantum gates with neutral atoms: Controlling collisional interactions in time dependent traps
- Quantum systems under frequency modulation
- Quantum control and entanglement using periodic driving fields
- Manipulation of Single Neutral Atoms in Optical Lattices
- Microwave Control of Atomic Motion in Optical Lattices
- Rapid Quantum Squeezing by Jumping the Harmonic Oscillator Frequency
- Ermakov-Lewis symmetry in photonic lattices
- Phase-coherent sensing of the center-of-mass motion of trapped-ion crystals
- Quadratic Time-dependent Quantum Harmonic Oscillator
- Robust optomechanical state transfer under composite phase driving
- Experimental demonstration of Gaussian boson sampling with displacement
- Invariant-based inverse engineering of time-dependent, coupled harmonic oscillators
- Exact solution of a time-dependent quantum harmonic oscillator with two frequency jumps via the Lewis-Riesenfeld dynamical invariant method
- Time-dependent harmonic potentials for momentum or position scaling
- Tailored Ion Beam for Precise Color Center Creation