[Paper Review] Acoustic Traps and Lattices for Electrons in Semiconductors

Martin J. A. Schuetz, Johannes Knoerzer+4 more|arXiv (Cornell University)|May 13, 2017

Neural Networks and Applications4 citations

TL;DR

This paper proposes a solid-state platform using surface acoustic waves (SAWs) to create tunable, stationary acoustic lattices that trap and control electrons in semiconductors. By leveraging a perturbative Floquet approach, it demonstrates that rapidly oscillating SAW-induced potentials can effectively form time-independent pseudo-lattices with reconfigurable spacing (~100 nm), enabling the simulation of strongly correlated fermionic Hubbard models at low temperatures with potential for quantum simulation and control.

ABSTRACT

We propose and analyze a solid-state platform based on surface acoustic waves (SAWs) for trapping, cooling and controlling (charged) particles, as well as the simulation of quantum many-body systems. We develop a general theoretical framework demonstrating the emergence of effective time-independent acoustic trapping potentials for particles in two- or one-dimensional structures. As our main example we discuss in detail the generation and applications of a stationary, but movable acoustic pseudo-lattice (AL) with lattice parameters that are reconfigurable in situ. We identify the relevant figures of merit, discuss potential experimental platforms for a faithful implementation of such an acoustic lattice, and provide estimates for typical system parameters. With a projected lattice spacing on the scale of 100nm, this approach allows for relatively large energy scales in the realization of fermionic Hubbard models, with the ultimate prospect of entering the low temperature, strong interaction regime. Experimental imperfections as well as read-out schemes are discussed.

Motivation & Objective

• To develop a scalable, on-chip platform for trapping and controlling electrons in solid-state systems using surface acoustic waves (SAWs).
• To overcome limitations of existing quantum dot and optical lattice approaches by enabling reconfigurable, low-temperature quantum simulation in semiconductors.
• To demonstrate the emergence of effective time-independent acoustic pseudo-lattices from time-periodic SAW potentials via a theoretical framework.
• To enable the realization of fermionic Hubbard models with tunable on-site interactions and lattice parameters in a solid-state environment.

Proposed method

• Utilizes counter-propagating SAWs generated by interdigital transducers (IDTs) on piezoelectric substrates to create a periodic, time-dependent electric potential for electrons in a 2DEG.
• Applies a perturbative Floquet theory to derive effective time-independent Hamiltonians that describe stable trapping potentials for electrons.
• Demonstrates that electron motion is adiabatically suppressed in rapidly oscillating potentials, leading to effective localization in potential minima.
• Models the system using a Mathieu-type stability analysis to ensure electron confinement and avoid heating from RF driving.
• Proposes experimental configurations with IDTs placed away from the trap center to minimize local heating and improve thermal management.
• Introduces a screening layer to tune Coulomb interactions between electrons, enabling control over interaction strength in many-body simulations.

Experimental results

Research questions

• RQ1 Can surface acoustic waves generate stable, time-independent effective potentials for electrons in semiconductors despite their inherent time-periodicity?
• RQ2 What are the key physical conditions and system parameters that allow for the formation of a reconfigurable acoustic pseudo-lattice with ~100 nm spacing?
• RQ3 How can heating from RF-driven IDTs be mitigated to preserve low-temperature operation and quantum coherence?
• RQ4 To what extent can electron spin decoherence due to hyperfine interactions be suppressed in such a system?
• RQ5 Can this platform simulate strongly correlated fermionic Hubbard models with tunable on-site repulsion and hopping?

Key findings

• The effective potential for electrons becomes time-independent when the SAW frequency is sufficiently high, enabling stable trapping via a Floquet-based effective Hamiltonian.
• A reconfigurable acoustic pseudo-lattice with lattice spacing ~100 nm can be achieved at SAW frequencies of ~20 GHz, enabling access to large energy scales.
• The system operates at low RF power levels (≤ -10 dBm, or 0.1 mW), minimizing heating and allowing compatibility with dilution refrigerators at ~100 mK.
• Nuclear spin decoherence, which limits electron spin coherence to ~15 ns in GaAs, can be mitigated if coherent spin exchange rates exceed 1/T₂*, a condition shown to be achievable.
• In nuclear spin-free systems like ²⁸Si/SiGe heterostructures, electron spin coherence times can exceed 100 µs, significantly enhancing prospects for quantum simulation.
• The use of pulsed driving schemes and remote IDT placement further suppresses local heating, ensuring effective temperature control on relevant experimental timescales.