Quantum control of Hubbard excitons

Abstract

Quantum control of the many-body wavefunction is a central challenge in quantum materials research, as it could yield a precise control knob to manipulate emergent phenomena. Floquet engineering, the coherent dressing of quantum states with periodic non-resonant optical fields, has become an important strategy for quantum control. Most applications to solid-state systems have targeted weakly interacting or single-ion states, leaving the manipulation of many-body wavefunctions largely unexplored. Here, we use Floquet engineering to achieve quantum control of a strongly correlated Hubbard exciton in the one-dimensional Mott insulator Sr$_2$CuO$_3$. A nonresonant midinfrared optical field coherently dresses the exciton wavefunction, driving its rotation between bright and dark states. We use resonant third-harmonic generation to quantify ultrafast $π/2$ rotations on the Bloch sphere spanned by these exciton states. Our work advances the quest towards programmable control of correlated states and exciton-based quantum sensing.

Figures (4)

• Figure 1: Hubbard exciton and optical nonlinearity of Sr$_2$CuO$_3$.a. Electrons in the half-filled Mott insulator Sr$_2$CuO$_3$ interact via onsite ($U$) and intersite ($V$) Coulomb repulsion and hop with amplitude $t$. Empty (holon) and doubly-occupied (doublon) sites form bound states, known as Hubbard excitons. b. On-chain electrons can hop left or right into degenerate excitonic basis states $|L\rangle$ and $|R\rangle$, resulting in nearly-degenerate even- ($|g\rangle$) and odd-parity ($|u\rangle$) excitonic wavefunctions. c. Reduced on-chain optical conductivity $\omega\sigma_1(\omega)$ of Sr$_2$CuO$_3$ at 295 K. The Hubbard exciton exhibits strong third-harmonic generation at resonance with the excitonic levels. d. The third harmonic emission involves transitions between ground ($|0\rangle$), odd ($|u\rangle$), and even ($|g\rangle$) excitonic states located below a unbound holon-doublon (HD) continuum. $\mu_{ug}$ and $\mu_{0u}$ are the transition dipoles between odd- and even- exciton states and between ground and odd excitons, respectively.
• Figure 2: Quantum control of the Hubbard exciton.a. Experimental midinfrared pump field (center energy 0.12 eV, $\Delta\omega/\omega\sim8\%$). b. The instantaneous pump field at each time delay mixes even- ($|g\rangle$) and odd-parity ($|u\rangle$) exciton wavefunctions, initiating a subcycle rotation of the quantum state on the Bloch sphere. Sufficiently strong pump fields can coherently and instantaneously rotate the wavefunction by angles of $\vartheta\simeq\pi$. The energies of the two nearly-degenerate states remain unperturbed to first order, and the Bloch vector length is preserved during the rotation. As the quantum state rotates, the subcycle third-harmonic yield decreases due to changes in the dipole matrix elements, vanishing at $\vartheta=\pi$. c. The cycle-integrated rotation corresponds to a reduction of the Bloch vector length and a partial suppression of the third-harmonic emission.
• Figure 3: Detecting the wavefunction rotation via third harmonic renormalization.a. Schematics of the experimental setup. A MIR pump (orange, $\hbar\Omega$) excites the sample at normal incidence, while a NIR probe (red, $\hbar\omega$) impinges at $60^\circ$ to generate a third harmonic (THG, purple) measured in reflection. All beams are polarized parallel to the chains ($E \parallel b$). b. Third harmonic spectra of a $0.59$ eV NIR probe at equilibrium (purple) and after a $0.12$ eV pump ($E_\mathrm{MIR}=1.8$ MV/cm, orange, $\Delta t=0$ fs). Spectra are normalized to the equilibrium maximum and fit to Gaussian profiles (thin solid lines). c. THG patterns as a function of NIR probe (top) and MIR pump (bottom) polarization angles. The NIR probe is kept fixed at 0.59 eV, while $E_{\mathrm{MIR}}=1.2$ MV/cm. The MIR polarization data is symmetrized by averaging the two branches $[0,\pi]$ and $[\pi,2\pi]$. Error bars are standard deviations, while the solid line is a $1-J_0(A_1\cos\theta)^4$ fit with $A_1=(0.597 \pm 0.010)$. d. Time-resolved differential THG intensity (circles) for $E_\mathrm{MIR}=1.8$ MV/cm, fit to a $322.2(2.2)$ fs Gaussian profile. Error bars represent one standard deviation. Dashed lines mark time delays at which we calculate the instantaneous pump-induced angular rotation $\vartheta$ of Hubbard excitons with a three-level model.
• Figure 4: Floquet sidebands of the Hubbard exciton.a. Periodic MIR driving of even- and odd-parity states generates Floquet replicas spaced by $\hbar\Omega$, which produce sidebands in the nonlinear response. Third-order susceptibility in- (purple) and out-of-equilibrium (orange) for a three-level system (3LS) including the ground state and two excitonic levels, alongside a full holon-doublon (HD) model incorporating holon-doublon continuum and experimental broadening. Driven susceptibility is computed for a MIR pump field $E_\mathrm{MIR}=1.85$ MV/cm. b. Third harmonic spectra for selected NIR probe energies at equilibrium (purple) and after a $0.12$ eV pump ($E_\mathrm{MIR}=0.8$ MV/cm, orange, $\Delta t=0$ fs). c. Experimental (red circles) and theoretical (HD, dashed purple line) differential THG intensity at fixed MIR field $E_\mathrm{MIR}=0.8$ MV/cm, showing suppression of the main THG resonance and emergence of a below-gap Floquet sideband. Experimental spectra are binned to 20 meV, and error bars are standard deviations of 7 independent measurements. d. Differential third-order nonlinearity ($\sqrt{|\Delta I_{3\omega} / I_{3\omega}|}\propto\Delta\chi^{(3)} / \chi^{(3)}$) at $\hbar\omega=0.59$ eV as a function of MIR field and instantaneous rotation angle from the HD Floquet model (red circles). White circles mark the special angles $\vartheta=\pi/4,\: 3\pi/8,\: \mathrm{and}\: \pi/2$.