Quantum control of Hubbard excitons

This study demonstrates the quantum control of a strongly correlated Hubbard exciton in the one-dimensional Mott insulator Sr$_2$CuO$_3$ by using nonresonant midinfrared Floquet engineering to drive ultrafast rotations between bright and dark states, as quantified by resonant third-harmonic generation.

The Gist

Imagine a crowded dance floor where pairs of dancers are tightly holding hands, but they are so crowded that they can't move freely. In the world of quantum physics, this is what happens inside a special material called a Mott insulator (specifically, a crystal named Sr₂CuO₃). Inside this material, electrons get stuck in pairs: one pair is a "double" (two electrons on one spot) and the other is a "hole" (an empty spot). When these two dance together, they form a "Hubbard exciton."

Usually, these dancing pairs have two distinct "moods" or states:

1. The "Bright" Mood: They are visible to light and can glow.
2. The "Dark" Mood: They are invisible to light and stay silent.

In this paper, the researchers wanted to see if they could act like a DJ and force these electron pairs to switch moods instantly, using light instead of music.

The Experiment: The Invisible DJ

The scientists used two types of laser pulses to control this dance:

1. The "Probe" (The Spotlight): A near-infrared laser pulse acts like a camera flash. It briefly wakes up the electron pairs and puts them in the "Bright" mood. If the pairs stay bright, the camera sees a flash of light (specifically, a third-harmonic glow).
2. The "Pump" (The DJ): A mid-infrared laser pulse acts as the DJ. It doesn't try to change the music (the energy of the electrons) directly. Instead, it creates a rhythmic, shaking field that "dresses" the dancers.

The Magic Trick: Spinning the Dance Floor

When the "DJ" laser turns on, it doesn't just shake the dancers; it forces the entire quantum wavefunction (the description of the pair's state) to rotate.

Think of the electron pair's state as a spinning top on a sphere (called a Bloch sphere).

• At the top of the sphere is the Bright state.
• At the bottom is the Dark state.

Normally, the top stays at the top. But when the researchers applied their specific laser field, they could spin the top.

• If they spun it a little bit, the top was still mostly bright, but a little dimmer.
• If they spun it 90 degrees (a quarter turn), it was half bright, half dark.
• If they spun it 180 degrees (a full flip), the top was now at the bottom: completely Dark.

How They Knew It Worked

The researchers watched the "camera flash" (the third-harmonic glow).

• Before the DJ: The flash was bright.
• After the DJ: As they increased the strength of the DJ's laser, the flash got dimmer and dimmer.
• The Proof: When they rotated the state by 90 degrees, the flash dropped significantly. When they rotated it fully, the flash almost vanished. This proved they had successfully turned a "Bright" electron pair into a "Dark" one and back again, purely by controlling the rhythm of the light.

They also saw "echoes" of the DJ's beat in the light they measured. Just as a spinning top creates a blur, the rapid rotation of the electron state created new, faint signals (called Floquet sidebands) that proved the state was being coherently driven by the laser, not just heated up or scrambled.

Why This Matters (According to the Paper)

The paper claims this is a major step forward because:

1. It works on "strongly correlated" systems: Most previous experiments only worked on simple, weakly interacting particles. This worked on a complex, tightly-knit group of electrons.
2. It's programmable: They showed they can rotate the state by any angle they want, not just on/off. This is like having a dimmer switch for quantum states rather than just a light switch.
3. It's fast: This happens in the blink of an eye (femtoseconds), much faster than the electrons naturally settle down.

In short, the researchers built a "quantum remote control" that can spin the state of a complex electron pair from visible to invisible and back again, all by tuning the frequency and strength of a laser beam. This opens the door to potentially programming the behavior of quantum materials with precise light pulses.

Technical Summary

Technical Summary: Quantum Control of Hubbard Excitons in Sr₂CuO₃

Problem Statement
Quantum control of many-body wavefunctions remains a central challenge in quantum materials research, particularly for strongly correlated systems. While Floquet engineering—the coherent dressing of quantum states with periodic non-resonant optical fields—has successfully manipulated weakly interacting band structures and single-ion states, its application to strongly correlated many-body wavefunctions is largely unexplored. A primary difficulty lies in distinguishing coherent wavefunction manipulation from competing phenomena such as energy shifts, band renormalization, and symmetry breaking. The authors identify Hubbard excitons in one-dimensional Mott insulators as an ideal platform to address this, as their few-level structure (comprising nearly degenerate even- and odd-parity states) allows for direct access to coherent evolution without the complexity of higher-dimensional systems.

Methodology
The study utilizes the one-dimensional Mott insulator Sr₂CuO₃, which hosts Hubbard excitons formed by bound holon-doublon pairs. The experimental approach combines ultrafast mid-infrared (MIR) pump pulses with resonant near-infrared (NIR) probe pulses to manipulate and detect the excitonic state.

• Excitation: Intense, non-resonant MIR pulses (centered at 0.12 eV, well below the Mott gap) are used to coherently dress the exciton wavefunction. This field drives Rabi oscillations between the optically bright, odd-parity state ($|u\rangle$) and the dark, even-parity state ($|g\rangle$).
• Detection: The evolving quantum state is probed via time-resolved resonant third-harmonic generation (THG). The NIR probe (centered around 0.59 eV) generates THG emission through three-photon absorption. Because THG efficiency depends critically on the transition dipoles coupling the ground state, the odd state, and the even state, the signal serves as a sensitive probe of the exciton's parity composition.
• Theoretical Framework: The authors employ a Floquet holon-doublon Hamiltonian and a simplified three-level model to simulate the third-order susceptibility ($\chi^{(3)}$). These models account for the full continuum of unbound holon-doublon states and experimental broadening, validated by time-dependent exact-diagonalization calculations.

Key Results

1. Coherent Wavefunction Rotation: The application of non-resonant MIR fields induces coherent rotations of the Hubbard exciton wavefunction on the Bloch sphere spanned by the even and odd parity states. The MIR field mixes the parity components, effectively rotating the state from the bright $|u\rangle$ state toward the dark $|g\rangle$ state.
2. THG Suppression and Renormalization: As the exciton population rotates into the dark state, the resonant THG signal is suppressed. The authors observed a suppression of up to 70% in THG intensity at a pump field strength of 1.8 MV/cm. The suppression follows a Gaussian temporal profile consistent with the convolution of the pump and probe pulses, and its polarization dependence ($1 - J_0^4$) confirms the Floquet dressing mechanism rather than multipole moment generation.
3. Floquet Sidebands: By scanning the NIR probe energy across the exciton resonance, the authors detected the emergence of a Floquet sideband below the Mott gap. While the main THG resonance at the exciton energy was suppressed by 50%, the signal below the gap was enhanced by 40%. This non-monotonic behavior quantitatively agrees with the theoretical prediction of Floquet sidebands arising from transitions involving dressed excitonic levels.
4. Arbitrary Angle Control: By varying the MIR pump field strength, the authors demonstrated control over the rotation angle ($\vartheta$) of the many-body wavefunction. The rotation angle increases with field strength, reaching a peak instantaneous angle of $\vartheta = \pi/2$ at 1.7 MV/cm. This represents a uniaxial rotation of the wavefunction by arbitrary angles, consistent with all-optical U(1) control.

Significance and Claims
The paper claims to establish a new regime of Floquet engineering in strongly correlated solids where wavefunction mixing dominates over energy shifts. By achieving deterministic, ultrafast rotations of a many-body wavefunction in a prototypical Mott insulator, the work demonstrates that Hubbard excitons can serve as a programmable quantum system.

• Quantum Control: The ability to rotate the wavefunction by arbitrary angles (including $\pi/2$) provides the minimal building blocks for programmable pulse sequences, such as Ramsey interferometry and dynamical decoupling, in solid-state systems.
• Quantum Sensing: The authors suggest that the high sensitivity of exciton energy and lineshape to electronic interactions, combined with field-dependent wavefunction rotation, could enable exciton-based quantum sensing. This includes probing local dielectric screening and implementing decoupling sequences to enhance sensitivity in systems with narrow excitonic linewidths.
• Future Directions: The work opens pathways for extending these control protocols to the terahertz regime to reduce field requirements and to systems with strong spin-orbit coupling to achieve full SU(2) control in the azimuthal plane.