Acoustic Traps and Lattices for Electrons in Semiconductors

We propose and analyze a solid-state platform based on surface acoustic waves 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 pseudolattice 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 $\sim 100\mathrm{nm}$, 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 readout schemes are discussed.

Popular Summary

The ability to trap and control atoms and molecules with electromagnetic fields has led to revolutionary advances in diverse fields such as biology, condensed-matter physics, and quantum information. These advances range from optical tweezers for probing the mechanical properties of DNA to the experimental realization of Bose-Einstein condensates, an exotic state of matter that arises when certain substances are cooled to near absolute zero. Meanwhile, improvements in the fabrication of semiconductor nanostructures have led to a proliferation of quasiparticles, an emergent behavior that arises from complex interactions among electrons and atoms. Researchers would like to trap quasiparticles to gain deeper insights into their properties and interactions. Semiconductor nanostructures known as quantum dots are excellent traps, but scaling them to encompass many particles is challenging. We propose a novel method for trapping and manipulating quasiparticles in solid-state matter.

Our proposal makes use of surface acoustic waves (SAW)—sound waves that traverse the surface of a material—thereby bringing the flexibility of electromagnetic traps to the solid-state setting and creating a new toolbox applicable to a broad class of systems. Our acoustic trapping mechanism is closely related to techniques used to trap ions, thus interconnecting two previously unrelated research fields. The SAW configuration shares the flexibility of optical lattices for atoms and may serve similarly as a basis to study many-body physics, albeit in unprecedented parameter regimes because of ultrahigh charge-to-mass ratios and long-ranged Coulomb interactions.

This technique enables a new approach to the realization of quantum simulators and synthetic quantum matter.

Figure 1

Exemplary schematic illustration of the setup. In a piezoelectric solid (PE) counterpropagating SAWs (as induced by standard IDTs deposited on the surface [19, 20]) generate a time-dependent, periodic electric potential for electrons confined in a conventional two-dimensional electron gas (2DEG). If the SAW frequency $\omega /2\pi =v_s/\lambda$ is sufficiently high (as specified in the main text), the electron’s potential landscape can effectively be described by a time-independent pseudolattice with a lattice spacing $a=\lambda /2$. The potential depth (lattice spacing) can be controlled conveniently via the power (frequency) applied to the IDTs, while an additional screening layer (not shown) allows for tuning the strength of the Coulomb interaction between the particles [23]. In more complex structures, the setup can consist of multiple layers on top of some substrate.

Figure 2

Approximate stability diagrams of the classical equation of motion in the low-$q$ (upper plot) and high-$q$ (lower plot) regimes, respectively. The dots denote trajectories corresponding to some exemplarily chosen parameter sets $(q,k_{B}T/E_S)$.

Figure 3

Exact numerical simulation [based on Eqs. (c37) and (5)] for the electron’s trajectory ${⟨\widehat{x}⟩}_t$ (solid black line), showing a slow secular motion with frequency ${\omega }_0$ that is superimposed by fast, small-amplitude micromotion oscillations. When disregarding micromotion, the dynamics can approximately be described by a simple damped harmonic oscillator with secular frequency ${\omega }_0$ (dashed red line). The initial state has been set as a coherent state with $⟨\widehat{\tilde{x}}⟩=0$, $⟨\widehat{\tilde{p}}⟩=0.01$. Other numerical parameters are $q=0.47$, $\gamma /{\omega }_0={10}^{-3}$, $k_{B}T/\hslash {\omega }_0={10}^{-1}$, ${\omega }_0/\omega \approx 0.17$. Inset: Position variance ${\sigma }_{\tilde{x}}^2=⟨{\widehat{\tilde{x}}}^2⟩-⟨\widehat{\tilde{x}}{⟩}^2$ at times when transient effects have decayed.

Figure 4

Speed of sound $v_s$ (left axis) and kinetic sound energy $E_S$ normalized to its value at $h=\lambda$ (right axis) in layered heterostructures made of gallium arsenide (aluminum nitride) and diamond. All results are given as a function of $h$, which denotes the thickness of the GaAs (AlN) layer. Results for the second SAW modes and heavy holes are shown. Squares and pentagons (triangles) denote the numerical results for a GaAs/diamond (AlN/diamond) heterostructure. $E_S(h=\lambda )\approx 32\mu \mathrm{eV}$ for GaAs/diamond ($\approx 205\mu \mathrm{eV}$ for AlN/diamond). The data points are connected by lines to guide the eye. The isolated data points at $h\approx 0.57\lambda$ denote an ultrahigh velocity PSAW mode in AlN/diamond (cf. Ref. [45]). Inset: Distribution of the piezoelectric potential at $f=12.2\mathrm{GHz}$ of a second SAW mode for a layer thickness of $h=0.2\mu \mathrm{m}$ in a GaAs/diamond heterostructure. The IDT finger spacing, hence the SAW wavelength, is set to be $\lambda =500\mathrm{nm}$. The results are obtained with the software package comsol.

Figure 5

Schematic illustration (top view, not to scale) for a quasistationary two-dimensional AL which can be controllably displaced in both $x$ and $y$ direction by adiabatically tuning the phases applied to the IDTs. The dashed (orange) box highlights a small sublattice consisting of just four lattice sites, before and after the adiabatic ramp.