Bloch-wave interferometry of driven quasiparticles in bulk GaAs

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Bloch-wave interferometry of driven quasiparticles in bulk GaAs

Seamus D. O'Hara, Joseph B. Costello, Qile Wu, Ken West, Loren Pfeiffer, and Mark S. Sherwin

Phys. Rev. B 109, 054308 – Published 20 February 2024

Abstract

We show that the polarizations of sidebands emitted from bulk gallium arsenide driven by a strong terahertz (THz) field while probed with a weak near-infrared laser can be viewed as interferograms from a Michelson-like interferometer for Bloch waves. The fringe contrast of an interferogram is a measure of the nonequilibrium dephasing of Bloch waves in this strongly driven system. An interferogram's oscillation frequency is determined by, among other factors, the THz field strength $F_{THz}$ and the reduced masses of electron-hole pairs. A simple analytic model brings all measured and calculated spectra into agreement with adjustment of only a single dephasing constant, and predicts the scaling of interferograms with $F_{THz}$ .

Received 19 May 2023
Revised 22 January 2024
Accepted 24 January 2024

DOI:https://doi.org/10.1103/PhysRevB.109.054308

Physics Subject Headings (PhySH)

Excitons

III-V semiconductors Nonequilibrium systems

Bloch wave theory Optical absorption spectroscopy Optical interferometry Photoluminescence Terahertz spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Seamus D. O'Hara ^1,2,*, Joseph B. Costello ^1,2, Qile Wu ^1,2, Ken West³, Loren Pfeiffer³, and Mark S. Sherwin ^1,2,†

¹Physics Department, University of California, Santa Barbara, California 93106, USA
²Institute for Terahertz Science and Technology, University of California, Santa Barbara, California 93106, USA
³Electrical Engineering Department, Princeton University, Princeton, New Jersey 08544, USA

^*seamuso@sas.upenn.edu
^†sherwin@physics.ucsb.edu

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Vol. 109, Iss. 5 — 1 February 2024

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Images

Figure 1
Description of high-order sideband generation (HSG) in bulk GaAs as a Michelson interferometer for Bloch waves. (a) An example of a sideband spectrum taken at THz field strength $F_{THz} = 70$ kV/cm with NIR laser frequency at red dashed line. (Inset) The crystal orientation of the GaAs crystal with respect to the THz field. (b) A representation of HSG in momentum space showing electron (E), heavy-hole (HH), and light-hole (LH) bands. (c) A Michelson interferometer for Bloch waves. The Roman numerals in (b) and (c) label the following processes. (i) A NIR laser is incident on the bulk GaAs. (ii) The bulk GaAs acts like a beam-splitter, converting the NIR laser beam into E-HH and E-LH pairs. (iii) In the two interferometer arms, Bloch waves of E-HH and E-LH pairs propagate along different k-space trajectories and acquire different phases. (iv) These Bloch waves merge at the beam-splitter and (v) sidebands are emitted. Bloch-wave interferograms of sideband polarizations are recorded by Stokes polarimetry with a quarter-wave plate (QWP) and a polarizer. (d) Stokes polarimetry and a Bloch-wave interferogram. (Top) Three normalized Stokes parameters ${\tilde{S}}_{1}, {\tilde{S}}_{2}$ , and ${\tilde{S}}_{3}$ corresponding to the sideband spectrum in (a). (Bottom) a Bloch-wave interferogram that is the sideband polarization as a function of sideband order $n$ . The polarization of the $n th$ -order sideband is represented as a normalized state in the basis of circular polarizations, $| E_{SB, n} 〉 = l (n) e^{i ϕ (n)} | L 〉 + r (n) | R 〉$ , where $l (n), r (n)$ , and $ϕ (n)$ are real functions of $n$ (see Appendix pp3-s2 for definitions of the basis states).
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Figure 2
Bloch-wave interferograms for different NIR polarizations and THz field strengths. (Top row) The left-handed circularly polarized component $[l^{2} (n)$ ] [see Eq. (2)]. (Bottom row) The relative phase $ϕ (n)$ between the left-handed and right-handed circularly polarized components of the sideband photons. Columns from left to right: four different polarization states of the NIR laser (cartoons in upper corners of top row), right-handed circularly polarized (first), left-handed circularly polarized (second), diagonal (third), and antidiagonal (fourth). The data were taken with three THz field strengths, 70.0 kV/cm (blue symbols), 52.5 kV/cm (green symbols), and 35.0 kV/cm (red symbols). The dashed lines represent the results calculated under the linear-in-time (LIT) approximation, with the bands representing a $\pm 7 %$ experimental error in THz field strength.
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Figure 3
Scaled Bloch-wave interferograms. The experimental data for $l^{2} (n)$ and $ϕ (n)$ shown in Fig. 2 are plotted as functions of a rescaled sideband order, $n \times λ^{- 2 / 5} [λ = F_{THz} / (70$ kV/cm)], with the scaling factor predicted from Eq. (6).
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Figure 4
An absorbance spectrum of the GaAs epilayer. The purple dashed line indicates the NIR wavelength used in experiments reported in this paper. The measurement was taken at the spot illuminated by a white light source (inset).
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Figure 5
Definition of the orientation angle $α_{n}$ and ellipticity angle $γ_{n}$ . The sign of the ellipticity angle $γ_{n}$ is defined with respect to the wave vector $k$ .
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Figure 6
Dynamical quantities calculated by using the LIT approximation (dashed line) and the numerical solutions with a sinusoidal (solid line) THz field for the E-H pairs, which produce a 32nd-order sideband. The results for different field strengths used in the experiment, 70 kV/cm (blue), 52.5 kV/cm (green), and 35 kV/cm (red), are all displayed. The left and right columns show quantities calculated for the E-HH and E-LH pairs, respectively. The top row shows the calculated x position for the holes (dark colors) and electrons (light colors). The second row shows the calculated wave vectors for the electrons (downward parabolas, associated with the left y axis, a = 5.56 $Å$ ) and the THz fields (lines, associated with the right y axis). The third row shows the calculated kinetic energies of the E-H pairs. The bottom row shows the calculated absolute values of the dynamic phases of the E-H pairs.
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