Floquet States Research Articles

Continuous broadband Rydberg receiver using AC Stark shifts and Floquet states

We demonstrate the continuous broadband microwave receivers based on AC Stark shifts and Floquet states of Rydberg levels in a cesium atomic vapor cell. The resonant transition frequency of two adjacent Rydberg states 78 S1/2 and 78 P1/2 is tuned based on AC Stark effect of 70 MHz radio frequency (RF) field that is applied outside the vapor cell. The use of the j=1/2 Rydberg states ensures that only a single mj sublevel is involved. The generated Rydberg Floquet states act to enhance the sensitivity of the AC-Stark-tuned states when the frequency is matched and further extend the bandwidths. We achieve microwave field measurements with over 1.172 GHz continuous frequency tuning and a sensitivity ranging from 280.2 nVcm−1Hz−1/2 to 14.6 μ Vcm−1Hz−1/2. The achieving of continuous frequency and high sensitivity microwave detection will promote the application of Rydberg receivers in the radar technique and wireless communication.

Floquet engineering of interparticle correlations in electron-hole few-body system for strong radial confinement

We investigate the effects of off-resonant THz-frequency laser light coupling to bound few-body electron-hole system, i.e. the exciton and negatively charged trion confined in quantum wire. To solve this problem, we first conduct a unitary Hennerberger-Kramers transformation of the Hamiltonian and diagonalize its perturbative approximation to obtain the exciton and trion Floquet states. Within this framework, the light-matter coupling renormalizes an attractiveehinteraction, leaving the repulsiveeeunchanged, thus modifying corresponding two-particle correlation energies. Generally, the correlation energy ofehwould exceed theeeone for a semiconductor material with strongly localized heavy holes. However, as the former is weakened by increasing laser intensity, this relation can be reversed. Consequently, the trion may dissociate unconventionally, the hole gradually decouples from still strongly interacting electrons, and adequate energy and optical spectra changes accompany this process. The energy levels of the exciton and trion Floquet states are raised, while their optical brightness smoothly decreases for stronger laser intensities. We also show this process can be further modified by breaking the mirror symmetry of wire with a static electric field, and then the occurrence of the avoided crossings between the lowest energy levels of the trion depends on the laser intensity. These anticrossings shall be observed experimentally, confirming thus the usefulness of Floquet engineering for fast manipulations of the few-particle states in electron-hole systems on a subpicosecond time scale.

Novel Quantum States of Exciton-Floquet Composites: Electron-Hole Entanglement and Information.

Coulomb exchange between distinct electron-hole modes, i.e., exciton and Floquet states, in two-dimensional semiconductors is explored. Coherent ultrafast mixing of the exciton and Floquet states under weak optical pumping is investigated through a theoretical description of time-resolved and angle-resolved photoemission spectroscopy (tr-ARPES) in an extended Haldane model that includes the electron-hole Coulomb interaction. Two branches of novel quantum states are found in the form of bosonic exciton-Floquet composites, which result from exchange coupling due to the Coulomb interaction. Furthermore, tr-ARPES could be directly employed for the density matrix element of the biparticle subsystem of photoelectron and hole, and electron-hole entanglement and information could be further explored. This finding suggests a unique platform to study the buildup and dephasing of novel exciton-Floquet composites and to resolve the information carried by them, which would enable the pursuit of new reconfigurable devices based on two-dimensional semiconductors.

Timelike Kasner singularities and Floquet states in 2+1d AdS/CFT

We consider a model of a holographic 2+1d CFT interacting with an oscillating background gauge field. It is solved by an AdS-Vaidya metric describing Ohmic heating of the boundary field theory. However, we also show that if timelike singularities of Kasner type are permitted then a time independent solution that may be interpreted as a Floquet state of the system can be constructed. In this state the system exhibits either Hall conductivity or kinetic induction, and we numerically evaluate the Kasner exponents for a range of boundary conditions. This model may contribute to the ongoing discussion on the validity and meaning of the Kasner metric in the AdS/CFT correspondence and its application in cosmology.

Observation of Floquet states and their dephasing in colloidal nanoplatelets driven by visible pulses

Observation of Floquet states and their dephasing in colloidal nanoplatelets driven by visible pulses

High harmonic Mach–Zehnder interferometer for probing sub-laser-cycle electron dynamics in solids

High harmonic emissions from crystalline solids contain rich information on the dynamics of electrons driven by intense infrared laser fields and have been intensively studied owing to their potential use as a probe of microscopic electronic structures. In particular, the ability to measure the temporal response of high harmonics may allow us to investigate electron dynamics directly. Here, we demonstrate a Mach–Zehnder high harmonic interferometer, where high harmonics are generated in each path of a Mach–Zehnder interferometer and an interferogram of them is captured. The high harmonic interferometer allows us to detect high harmonic signals with higher sensitivity than conventional high harmonic intensity measurements, and achieve a relative time resolution between the target and reference high harmonics of less than 150 attoseconds, which is sufficient to track sub-cycle dynamics of electrons in solids. Using high harmonic interferometry, we succeeded in capturing the real time dynamics of Floquet states in WSe2, whose indirect signature has so far been caught only by time-averaged measurements. Our simple technique could enable to access attosecond electron dynamics in solids.

Floquet systems with continuous dynamical symmetries: characterization, time-dependent noether charge, and solvability

We study quantum Floquet (periodically-driven) systems having continuous dynamical symmetry (CDS) consisting of a time translation and a unitary transformation on the Hilbert space. Unlike the discrete ones, the CDS strongly constrains the possible Hamiltonians H(t) and allows us to obtain all the Floquet states by solving a finite-dimensional eigenvalue problem. Besides, Noether’s theorem leads to a time-dependent conservation charge, whose expectation value is time-independent throughout evolution. We exemplify these consequences of CDS in the seminal Rabi model, an effective model of a nitrogen-vacancy center in diamonds without strain terms, and Heisenberg spin models in rotating fields. Our results provide a systematic way of solving for Floquet states and explain how they avoid hybridization in quasienergy diagrams.

Half-quantized Hall states with C=3/2 exited by chiral photons

The topology of Hilbert space in semiconductor quantum wells (QW) can become non-trivial when excited by an electromagnetic wave. It means the quasi-energy bands acquire a nonzero integer Floquet-Chern number even if QW is trivial in the equilibrium. We analyze electron-photon interaction in the Floquet state and identify dynamical quantum phases characterized by half-quantized Floquet-Chern numbers. The non-integer topology depends on which equilibrium state is exposed to illumination. Trivial III-V semiconductor QW's such as AlGaAs and AlGaN, being resonantly illuminated, generate the dynamical index |CF|=1/2, similar to a gapless quantum anomalous semimetal (QAS) in equilibrium. Excitation of 2D topological insulator CdHgTe reveals |CF|=3/2 - the index stemmed exclusively from interaction with chiral photons. Comparing results obtained in continuous and full-Brillouin zone (BZ) models, we conclude that high-momentum regions in BZ contribute to the dynamical half-quantized topology. Results indicate that by manipulating parameters of external force, one can bring inverted-gap QW into a non-equilibrium state with a high topological non-integer charge |CF|=3/2. We present the phase diagram, which includes all dynamical states of non-trivial topology.

Localized Floquet states in gated bilayer graphene induced by a focused optical beam with orbital angular momentum

Localized Floquet states in gated bilayer graphene induced by a focused optical beam with orbital angular momentum

Spin–orbit coupling effects on localization and correlated tunneling for two interacting bosons in a double-well potential

We theoretically study the tunneling dynamics of two interacting spin–orbit-coupled (SOC) atoms trapped in a periodically perturbed double-well potential. We find that the phenomenon of coherent destruction of tunneling (CDT) can exist only for certain values of SOC, and two different mechanisms for the appearance of CDT are identified in this system. One is the conventional CDT resulting from quasi-energy degeneracy, while the other CDT originates from the dark Floquet state with zero quasi-energy for all values of the driving parameters. We discover that under double modulation combining the double-well potential shaking and a time-periodic Zeeman field, it is possible to realize spin-flipping single-atom Rabi tunneling and the CDT induced by the dark Floquet state at any value of SOC strength, which is not accessible with a single-drive field. Furthermore, we show that the detuning of Zeeman field with respect to the multiphoton energy is particularly significant in the case of the correlated two-particle tunneling mediated by SOC. We expect that these results will stimulate further exploration of the many-body dynamics in the interacting systems and expand the possibilities for manipulating the spin dynamics.

Gottesman-Kitaev-Preskill State Preparation Using Periodic Driving.

The Gottesman-Kitaev-Preskill (GKP) code may be used to overcome noise in continuous variable quantum systems. However, preparing GKP states remains experimentally challenging. We propose a method for preparing GKP states by engineering a time-periodic Hamiltonian whose Floquet states are GKP states. This Hamiltonian may be realized in a superconducting circuit comprising a SQUID shunted by a superinductor and a capacitor, with a characteristic impedance twice the resistance quantum. The GKP Floquet states can be prepared by adiabatically tuning the frequency of the external magnetic flux drive. Wepredict that highly squeezed >11.9 dB (10.8dB) GKP magic states can be prepared on a microsecond timescale, given a quality factor of 10^{6} (10^{5}) and flux noise at typical rates.

Effective versus Floquet theory for the Kerr parametric oscillator

Parametric gates and processes engineered from the perspective of the static effective Hamiltonian of a driven system are central to quantum technology. However, the perturbative expansions used to derive static effective models may not be able to efficiently capture all the relevant physics of the original system. In this work, we investigate the conditions for the validity of the usual low-order static effective Hamiltonian used to describe a Kerr oscillator under a squeezing drive. This system is of fundamental and technological interest. In particular, it has been used to stabilize Schrödinger cat states, which have applications for quantum computing. We compare the states and energies of the effective static Hamiltonian with the exact Floquet states and quasi-energies of the driven system and determine the parameter regime where the two descriptions agree. Our work brings to light the physics that is left out by ordinary static effective treatments and that can be explored by state-of-the-art experiments.

Anomalous Luttinger equivalence between temperature and curved spacetime: From black holes to thermal quenches

Building on the idea of Tolman and Ehrenfest that heat has weight, Luttinger established a deep connection between gravitational fields and thermal transport. However, this relation does not include anomalous quantum fluctuations that become paramount in strongly curved spacetime. In this work, we revisit the celebrated Tolman-Ehrenfest and Luttinger relations and show how to incorporate the quantum energy scales associated with these fluctuations, captured by gravitational anomalies of quantum field theories. We point out that such anomalous fluctuations naturally occur in the quantum atmosphere of a black hole. Our results reveal that analogous fluctuations are also observable in thermal conductors in flat-space time provided local temperature varies strongly. As a consequence, we establish that the gravitational anomalies manifest themselves naturally in non-linear thermal response of a quantum wire. In addition, we propose a systematic way to identify thermal analogues of black hole’s anomalous quantum fluctuations associated to gravitational anomalies. We identify their signatures in propagating energy waves following a thermal quench, as well as in the energy density of heating Floquet states induced by repeated thermal quenches.

Investigating the impact of polarization on surface plasmon polariton characteristics in plasmonic waveguides under periodic driving fields

This study examines the impact of polarization in the driving field on the surface plasmon polariton (SPP) modes within plasmonic waveguides under the influence of a periodic driving field. Addressing a significant knowledge gap in the existing literature, we present a comprehensive investigation employing Floquet engineering techniques, with a specific emphasis on elliptically polarized fields as the dressing field. Our analysis reveals that the use of generalized Floquet states allows us to derive Floquet states for specific polarized dressing fields, such as linear, left-handed circular, and right-handed circular polarization. Remarkably, we demonstrate that Floquet states depend on the chirality of the dressing field’s polarization. Employing the Floquet-Fermi golden rule, we assess electron transport under various polarization types and find that the specific polarization type influence electron transport properties. However, we establish that the chirality of the polarization of the dressing field does not impact the transport properties. During our numerical analysis, we assess the alterations in SPP characteristics arising from two distinct types of polarization in dressing fields: linear polarization and circular polarization. Our results underscore the potential of employing a dressing field to effectively mitigate the propagation losses of SPPs in plasmonic metals, with the extent of improvement contingent on the specific polarization type. To quantify the performance enhancements of commonly used plasmonic metals under linearly and circularly polarized dressing fields, we employ a figure of merit (FoM). This study offers insights into the practical utilization of periodic driving fields as a powerful tool in advancing plasmonic communication within chip-scale environments.

Tracking electron motion within and outside of Floquet bands from attosecond pulse trains in time-resolved ARPES

Floquet engineering has recently emerged as a technique for controlling material properties with light. Floquet phases can be probed with time- and angle-resolved photoelectron spectroscopy (Tr-ARPES), providing direct access to the laser-dressed electronic bands. Applications of Tr-ARPES to date focused on observing the Floquet-Bloch bands themselves, and their build-up and dephasing on sub-laser-cycle timescales. However, momentum and energy resolved sub-laser-cycle dynamics between Floquet bands have not been analyzed. Given that Floquet theory strictly applies in time-periodic conditions, the notion of resolving sub-laser-cycle dynamics between Floquet states seems contradictory—it requires probe pulse durations below a laser cycle that inherently cannot discern the time-periodic nature of the light-matter system. Here we propose to employ attosecond pulse train probes with the same temporal periodicity as the Floquet-dressing pump pulse, allowing both attosecond sub-laser-cycle resolution and a proper projection of Tr-ARPES spectra on the Floquet–Bloch bands. We formulate and employ this approach in ab-initio calculations in light-driven graphene. Our calculations predict significant sub-laser-cycle dynamics occurring within the Floquet phase with the majority of electrons moving within and in-between Floquet bands, and a small portion residing and moving outside of them in what we denote as ‘non-Floquet’ bands. We establish that non-Floquet bands arise from the pump laser envelope that induces non-adiabatic electronic excitations during the pulse turn-on and turn-off. By performing calculations in systems with poly-chromatic pumps we also show that Floquet states are not formed on a sub-laser-cycle level. This work indicates that the Floquet-Bloch states are generally not a complete basis set for sub-laser-cycle dynamics in steady-state phases of matter.

Unified light-matter Floquet theory and its application to quantum communication

Periodically driven quantum systems can exhibit a plethora of intriguing nonequilibrium phenomena that can be analyzed using Floquet theory. Naturally, Floquet theory is employed to describe the dynamics of atoms interacting with intense laser fields. However, this semiclassical analysis cannot account for quantum-optical phenomena that rely on the quantized nature of light. In this paper, we take a significant step to go beyond the semiclassical description of atom-photon coupled systems by unifying Floquet theory with quantum optics using the framework of full-counting statistics. This is achieved by introducing counting fields that keep track of the photonic dynamics. This formalism, which we dub “photon-resolved Floquet theory” (PRFT), is based on two-point tomographic measurements, instead of the two-point projective measurements used in standard full-counting statistics. Strikingly, the PRFT predicts the generation of macroscopic light-matter entanglement when atoms interact with multimode electromagnetic fields, thereby leading to complete decoherence of the atomic subsystem in the basis of the Floquet states. This decoherence occurs rapidly in the optical-frequency regime, but is negligible in the radio-frequency regime. Our results thus pave the way for the design of efficient quantum memories and quantum operations. Finally, employing the PRFT, we propose a quantum-communication protocol that can significantly outperform the state-of-art few-photon protocols by two orders of magnitude or better. The PRFT potentially leads to insights in various Floquet settings including spectroscopy, thermodynamics, quantum metrology, and quantum simulations. Published by the American Physical Society 2024

Strategies for phase matching control in a multidimensional Floquet state spectroscopy.

Floquet state spectroscopy is an optical analogue of multiple quantum coherence nuclear magnetic resonance (MQC-NMR). Tunable ultrafast excitation pulses resonantly excite multiple states in a sample to form the Floquet state. The Floquet state emits multiple coherent beams at frequencies and in directions that conserve energy and momenta. The different output beams differ in the time ordering and coherences created by the excitation beams. They correspond to the different methodologies in the NMR family. Isolating a specific beam and monitoring the output intensity as a function of excitation frequencies creates multidimensional spectra containing cross-peaks between coupled states. The frequency range of the multidimensional spectra is limited by phase matching constraints. This paper presents a new, to the best of our knowledge, active phase matching strategy that increases the versatility of multidimensional Floquet state spectroscopy through both longer sample path lengths and larger spectral ranges.

Destabilization of spin-Peierls phase via a charge-spin modulated Floquet state induced by intramolecular vibrational excitation

The electronic state control using a periodic light field is one of the central subjects in photophysics. In molecular solids, intramolecular vibrations sometimes couple to intermolecular electron transfer, thus modulating electron and spin densities of each molecule. Here, we show that in a quasi-one-dimensional molecular solid K-tetracyanoquinodimethane (TCNQ) in which TCNQ molecules are dimerized by the spin-Peierls mechanism, an intramolecular vibrational excitation with a phase-locked mid-infrared pulse induces a charge-spin modulated Floquet state, which destabilizes the spin-Peierls phase. By detecting reflectivity changes of the intramolecular transition band along the mid-infrared electric field with 6.6-fs probe pulses, we detected high-frequency oscillations reflecting electron- and spin-density modulations synchronized with intramolecular vibrations. More significantly, we observed an oscillation of ~110 cm−1 due to a dimeric mode driven by a decrease in spin-Peierls dimerization. This dimerization reduction was confirmed by measuring transient reflectivity changes of the Mott-gap transition band. These results demonstrate the effectiveness of intramolecular vibrational excitation as a method for Floquet engineering in molecular solids.

Electromagnetically induced transparency spectra of cesium Rydberg atoms decorated by radio-frequency fields

<sec>The large electric dipole moment of the Rydberg atom allows for strong coupling with weak electric fields, and is widely used in electric field measurements because of its reproducibility, precision and stability. The combination of Rydberg atoms and electromagnetically induced transparency (EIT) technology has been used for detecting and characterizing radio-frequency (RF) electric fields. </sec><sec>In this work, by selecting probe light (852 nm), dressed light (1470 nm), and coupled light (780 nm), the Rydberg state (49<i>P</i><sub>3/2</sub>) of Cs atom is prepared by using a three-photon excitation scheme through using all-infrared light excitation of Rydberg atoms. We experimentally observe the EIT spectra of the Rydberg states decorated by radio-frequency electric fields, which optically detects Rydberg atoms. The effect of the amplitude and frequency of the RF electric field on the spectrum is explored in light of changes in the EIT spectrum. The results show that in the region of weak electric field, only the ac Stark energy shift and spectral broadening occur. As the electric field is further enhanced, the sideband phenomenon occurs in both the primary peak and secondary peak of the EIT. In the region of strong field, the Rydberg energy level produces a series of Floquet states with higher-order terms, as well as state shifting and mixing, resulting in asymmetry in the spectra of the EIT sideband peaks. The effect of frequency on the shielding effect of the Cs vapor cell is further discussed based on the shift of the main peak of the EIT.</sec><sec>The demodulation of the electric field in a range of 50 Hz–1 kHz with a fidelity of 95% is achieved by modulating the low-frequency electric field to the RF electric field. The results can provide valuable references for spectral detection and traceable measurements of low-frequency electric fields.</sec>

Floquet engineering of selective magnon–magnon coupling in synthetic antiferromagnets

Floquet engineering is a widely applied method for temporally periodic driving in various quantum systems, capable of inducing emergent phenomena, such as Floquet states, Floquet topological insulators, and temporal crystals. In this work, we study the selective magnon–magnon coupling between sidebands by introducing Floquet engineering into magnonic system: coupling between Floquet sidebands occurs only when there is an odd order difference. In addition to the coherent coupling between the optical and acoustic modes in synthetic antiferromagnet, a Floquet coupling is observed as the secondary splitting of the two hybridized magnon modes. The splitting width of Floquet coupling exhibits different dependence with driving amplitude, i.e., linearly increasing for weak driving regime and nonlinearly varying for strong driving regime. Specifically, the nonlinear dependence arises from the coupling between hybridized sidebands that exhibit odd order differences in their components. Our findings could promote the further development of Floquet magnonics and its application for quantum information.