[Paper Review] Nonclassical light generation and control from laser-driven semiconductor intraband excitations

Ivan Gonoskov, René Sondenheimer+4 more|arXiv (Cornell University)|Nov 11, 2022

Laser-Matter Interactions and Applications4 citations

TL;DR

This paper proposes a quantum optical framework for high-harmonic generation (HHG) in semiconductors driven by intense laser fields, showing that intraband electron dynamics induce nonlinear coupling between fundamental and harmonic light modes. The key result is the intrinsic generation of multipartite entanglement across all optical modes, enabling scalable photonic resource states for quantum information processing with broad spectral coverage.

ABSTRACT

We investigate the generation of higher-order harmonics from a quantum optics perspective via the interaction of a semiconductor with a coherent pump field focusing on the regime where strong-field intraband excitations dominate. The related Schrödinger equation for the system is solved approximately and the classical and quantum characteristics of the fundamental light mode as well as the higher frequency modes are analyzed. We find intricate but sufficiently mild modifications of the fundamental mode and coherent displacements depending on the position quadrature component of the driving laser field for the harmonic modes within our approximations due to the intricate induced nonlinear interactions. Similar to high-harmonic generation in atoms, all radiation field modes are entangled, allowing for potential novel protocols for quantum information processing with high photon numbers over a large range of frequencies.

Motivation & Objective

• To develop a quantum mechanical description of high-harmonic generation (HHG) in semiconductors driven by intense laser fields, focusing on intraband transitions.
• To analyze the classical and quantum properties of the emitted radiation fields, particularly the non-Gaussian and entangled nature of the generated modes.
• To investigate how nonlinear band dispersion in semiconductors leads to structured, nontrivial modifications of the radiation field beyond classical expectations.
• To explore the potential of laser-driven intraband HHG as a source of complex, entangled photonic states for quantum information processing.
• To validate the analytical model against classical solutions derived from semiconductor-Maxwell-Bloch equations.

Proposed method

• A first-order approximation is used to solve the Schrödinger equation for the coupled system of a semiconductor and multi-mode quantized light, incorporating nonlinear band dispersion effects.
• The Hamiltonian is constructed with field operators entering nonlinearly via the band dispersion, differing from the linear dipole coupling in atomic HHG.
• Analytical solutions are derived for coherent state displacements in harmonic modes, parameterized by the position quadrature of the pump field.
• Conditional state projection via the operator $\hat{\bm{1}} - \ket{G_0}\bra{G_0}$ isolates the HHG-generated state, removing the vacuum component.
• The resulting state is expressed in position representation to demonstrate nonseparability and entanglement across all optical modes.
• The solution is validated by comparison with numerical solutions from the semiconductor-Maxwell-Bloch equations in the classical regime.

Experimental results

Research questions

• RQ1 How do nonlinear intraband electron dynamics in semiconductors modify the quantum state of emitted light in high-harmonic generation?
• RQ2 To what extent do the quantum properties of the fundamental and harmonic modes become entangled under strong-field intraband excitation?
• RQ3 What is the role of the pump field's position quadrature in shaping the displacement amplitudes of harmonic modes?
• RQ4 How do the non-Gaussian modifications of the radiation field arise from the nonlinear band dispersion in the semiconductor?
• RQ5 Can the HHG process in semiconductors generate usable multipartite entangled photonic states for quantum information applications?

Key findings

• The generated radiation field exhibits non-Gaussian modifications due to nonlinear interactions, yet expectation values of functions of the pump field's position quadrature remain unchanged.
• The harmonic modes are coherently displaced in a nonlinear fashion dependent on the pump field's position quadrature, with $|\alpha_j|^2 \sim N_0$ in the minimum of the intraband potential.
• The HHG process naturally produces multipartite entanglement between all optical modes, as demonstrated by the nonseparable structure of the conditioned state $\braket{\vec{Q}}{G_{\mathrm{HHG}}}$.
• The entangled state structure is analogous to that in atomic HHG but with stronger dependence on the pump field's quadrature due to nonlinear band dispersion.
• The system generates high photon numbers across a broad spectral range—from infrared to ultraviolet—making it suitable for quantum information applications.
• The analytical solution is consistent with classical SMBE simulations, validating the approach within the first-order approximation and under the assumed model constraints.