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A central paradigm of non-equilibrium physics concerns the dynamics of heterogeneity and disorder, impacting processes ranging from the behavior of glasses to the emergent functionality of active matter. Understanding these complex mesoscopic systems requires probing the microscopic trajectories associated with irreversible processes, the role of fluctuations and entropy growth, and the timescales on which non-equilibrium responses are ultimately maintained. Approaches that illuminate these processes in model systems may enable a more general understanding of other heterogeneous non-equilibrium phenomena, and potentially define ultimate speed and energy cost limits for information processing technologies. Here, we apply ultrafast single shot x-ray photon correlation spectroscopy to resolve the non-equilibrium, heterogeneous, and irreversible mesoscale dynamics during a light-induced phase transition. This approach defines a new way of capturing the nucleation of the induced phase, the formation of transient mesoscale defects at the boundaries of the nuclei, and the eventual annihilation of these defects, even in systems with complex polarization topologies. A non-equilibrium response spanning >10 orders of magnitude in timescales is observed, with multistep behavior similar to the plateaus observed in supercooled liquids and glasses. We show how the observed time-dependent long-time correlations can be understood in terms of the stochastic dynamics of domain walls, encoded in effective waiting-time distributions with power-law tails. This work defines new possibilities for probing the non-equilibrium and correlated dynamics of disordered and heterogeneous media.

Mott metal-insulator transitions possess electronic, magnetic, and structural degrees of freedom promising next generation energy-efficient electronics. We report a previously unknown, hierarchically ordered state during a Mott transition and demonstrate correlated switching of functional electronic properties. We elucidate in-situ formation of an intrinsic supercrystal in a Ca2RuO4 thin film. Machine learning-assisted X-ray nanodiffraction together with electron microscopy reveal multi-scale periodic domain formation at and below the film transition temperature (TFilm ~ 200-250 K) and a separate anisotropic spatial structure at and above TFilm. Local resistivity measurements imply an intrinsic coupling of the supercrystal orientation to the material's anisotropic conductivity. Our findings add an additional degree of complexity to the physical understanding of Mott transitions, opening opportunities for designing materials with tunable electronic properties.

Rydberg microwave (MW) sensors are superior to conventional antenna-based techniques because of their wide operating frequency range and outstanding potential sensitivity. Here, we demonstrate a Rydberg microwave receiver with a high sensitivity of $62\,\mathrm{nV} \mathrm{cm}^{-1} \mathrm{Hz}^{-1/2}$ and broad instantaneous bandwidth of up to $10.2\,\mathrm{MHz}$. Such excellent performance was achieved by the amplification of one generated sideband wave induced by the strong coupling field in the six-wave mixing process of the Rydberg superheterodyne receiver, which was well predicted by our theory. Our system, which possesses a uniquely enhanced instantaneous bandwidth and high-sensitivity features that can be improved further, will promote the application of Rydberg microwave electrometry in radar and communication.

We theoretically study the effect of quantum statistics of the light field on the quantum enhancement of parameter estimation based on cat state input the SU(1,1) interferometer. The phase sensitivity is dependent on the relative phase $\theta$ between two coherent states of Schr\"{o}dinger cat states. The optimal sensitivity is achieved when the relative phase is $\pi$% , i.e., odd coherent states input. For a coherent state input into one port, the phase sensitivity of the odd coherent state into the second input port is inferior to that of the squeezed vacuum state input. However, in the presence of losses the Schr\"{o}dinger cat states are more resistant to loss than squeezed vacuum states. As the amplitude of Schr\"{o}dinger cat states increases, the quantum enhancement of phase sensitivity decreases, which shows that the quantum statistics of Schr\"{o}dinger cat states tends towards Poisson statistics from sub-Poisson statistics or super-Poisson statistics., Comment: 8 pages, 5 figures. arXiv admin note: text overlap with arXiv:2302.09823

The quantum Fisher information (QFI) in SU(2) and SU(1,1) interferometers was considered, and the QFI-only calculation was overestimated. In general, the phase estimation as a two-parameter estimation problem, and the quantum Fisher information matrix (QFIM) is necessary. In this paper, we theoretically generalize the model developed by Escher et al [Nature Physics 7, 406 (2011)] to the QFIM case with noise and study the ultimate precision limits of SU(2) and SU(1,1) interferometers with photon losses because photon losses as a very usual noise may happen to the phase measurement process. Using coherent state and squeezed vacuum state as a specific example, we numerically analyze the variation of the overestimated QFI with the loss coefficient, and find its disappearance and recovery phenomenon.

Ferroelectrics have a spontaneous electrical polarization that is arranged into domains and can be reversed by an externally applied field. This high versatility makes them useful in enabling components such as capacitors, sensors, and actuators. The key to tuning their dielectric, piezoelectric, and electromechanical performance is to control the domain structure and the dynamics of the domain walls. In fixed compositions, this is often realized by chemical doping. In addition, structural and microstructural parameters, such as grain size, degree of crystallographic texture or porosity play a key role. A major breakthrough in the field came with the fundamental understanding of the link between the local electric and mechanical driving forces and domain wall motion. Here, the impact of structure and microstructure on these driving forces is reviewed and an engineering toolbox is introduced. An overview of advances in the understanding of domain wall motion on the micro- and nanoscale is provided and discussed in terms of the macroscopic functional performance of polycrystalline ferroelectrics/ferroelastics. In addition, a link to theoretical and computational models is established. The review concludes with a discussion about beyond state-of-the-art characterization techniques, new approaches, and future directions toward non-conventionally ordered ferroelectrics for next-generation nanoelectronics and energy-storage applications.

The SU (1,1)-type atom-light hybrid interferometer (SALHI) is a kind of interferometer that is sensitive to both the optical phase and atomic phase. However, the loss has been an unavoidable problem in practical applications and greatly limits the use of interferometers. Visibility is an important parameter to evaluate the sensing performance of interferometers. Here, we experimentally demonstrate the mitigating effect of the loss on visibility of the SALHI via asymmetric gain optimization, where the maximum threshold of loss to visibility close to $100\%$ is increased. Furthermore, we theoretically find that the optimal condition for the largest visibility is the same as that for the enhancement of signal-to-noise ratio (SNR) to the best value in the presence of losses using the intensity detection, indicating that the visibility can act as an experimental operational criterion for SNR improvement in practical applications. Improvement of the interference visibility means achievement of SNR enhancement. Our results provide a significant foundation for practical application of the SALHI in radar and ranging measurements., Comment: 4 figures

Bulk single-crystal relaxor-ferroelectrics, like Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT), are widely known for their large piezoelectricity. This is attributed to polarization rotation which is facilitated by the presence of various crystal symmetries for compositions near a morphotropic phase boundary (MPB). Relaxor-ferroelectric thin films, which are necessary for low-voltage applications, suffer a reduction in their piezoelectric response due to clamping by the passive substrate. To understand the microscopic behavior of this adverse phenomenon, we employ AC electric field driven in-operando synchrotron x-ray diffraction (XRD) on patterned device structures to investigate the piezoelectric domain behavior under an electric field for both a clamped (001) PMN-PT thin film on Si and a (001) PMN-PT membrane released from its substrate. In the clamped film, the substrate inhibits the field induced rhombohedral (R) to tetragonal (T) phase transition resulting in a reversible R to Monoclinic (M) transition with a reduced longitudinal piezoelectric coefficient d33 < 100 pm/V. Releasing the film from the substrate results in recovery of the R to T transition and results in a d33 > 1000 pm/V. Using diffraction with spatial mapping, we find that lateral constraints imposed by the boundary between active and inactive material also inhibits the R to T transition. Phase-field calculations on both clamped and released PMN-PT thin films simulate our experimental findings. Resolving the suppression of thin film piezoelectric response is critical to their application in piezo-driven technologies.

Strain-mediated magnetoelectric (ME) coupling in ferroelectric (FE) / ferromagnetic (FM) heterostructures offers a unique opportunity for both fundamental scientific research and low power multifunctional devices. Relaxor-ferroelectrics, like (1-x)Pb(Mg1/3Nb2/3)O3-(x)PbTiO3 (PMN-xPT), are ideal FE layer candidates due to their giant piezoelectricity. But thin films of PMN-PT suffer from substrate clamping which substantially reduces piezoelectric in-plane strains. Here we present the first demonstration of low voltage ME coupling in an all-thin-film heterostructure which utilizes the anisotropic strains induced by the (011) orientation of PMN-PT. We completely remove PMN-PT films from their substrate and couple with FM Ni overlayers to create membrane PMN-PT/Ni heterostructures showing 90 degree Ni magnetization rotation with 3V PMN-PT bias, much less than the bulk PMNPT ~100V requirement. Scanning transmission electron microscopy and phase-field simulations clarify the membrane response. These results provide a crucial step towards understanding the microstructural behavior of PMN-PT thin films for use in piezo-driven magnetoelectric heterostructures.

The control of the in-plane domain evolution in ferroelectric thin films is not only critical to understanding ferroelectric phenomena but also to enabling functional device fabrication. However, in-plane polarized ferroelectric thin films typically exhibit complicated multi-domain states, not desirable for optoelectronic device performance. Here we report a strategy combining interfacial symmetry engineering and anisotropic strain to design single-domain, in-plane polarized ferroelectric BaTiO$_3$ thin films. Theoretical calculations predict the key role of the BaTiO$_3$ / PrScO$_3$ (110)$_O$ substrate interfacial environment, where anisotropic strain, monoclinic distortions, and interfacial electrostatic potential stabilize a single-variant spontaneous polarization. A combination of scanning transmission electron microscopy, piezoresponse force microscopy, ferroelectric hysteresis loop measurements, and second harmonic generation measurements directly reveals the stabilization of the in-plane quasi-single-domain polarization state. This work offers design principles for engineering in-plane domains of ferroelectric oxide thin films, which is a prerequisite for high performance optoelectronic devices.

Quantum non-demolition (QND) measurement is an important tool in the field of quantum information processing and quantum optics. The atom-light hybrid interferometer is of great interest due to its combination of atomic spin wave and optical wave, which can be utilized for photon number QND measurement via the AC-Stark effect. In this paper, we present an SU(1,1)-SU(2)-concatenated atom-light hybrid interferometer, and theoretically study the QND measurement of photon number. Compared to the traditional SU(2) interferometer, the signal-to-noise ratio (SNR) in a balanced case is improved by a gain factor of the nonlinear Raman process (NRP) in this proposed interferometer. Furthermore, the condition of high-quality of QND measurement is analyzed. In the presence of losses, the measurement quality is reduced. We can adjust the gain parameter of the NRP in readout stage to reduce the impact due to losses. Moreover, this scheme is a multiarm interferometer, which has the potential of multiparameter estimation with many important applications in the detection of vector fields, quantum imaging and so on.

We theoretically studied the quantum Cram\'{e}r-Rao bound of an actively correlated Mach-Zehnder interferometer (ACMZI), where the quantum Fisher information obtained by the phase-averaging method can give the proper phase-sensing limit without any external phase reference. We numerically calculate the phase sensitivities with the method of homodyne detection and intensity detection in the presence of losses. Under lossless and very low loss conditions, the ACMZI is operated in a balanced case to beat the standard quantum limit (SQL). As the loss increases, the reduction in sensitivity increases. However within a certain range, we can adjust the gain parameters of the beam recombination process to reduce the reduction in sensitivity and realize the sensitivity can continue to beat the SQL in an unbalanced situation. Our scheme provides an optimization method of phase estimation in the presence of losses.

In recent years, unshielded atomic systems have been attracting researchers' attention, in which decoherence is one of the major problems, especially for high precision measurements. The nonlinear Zeeman effect and magnetic field gradient are the main decoherence sources of atomic electron spin in Earth-field range. Here, we propose a method to cancel out the two dominant broadening effects simultaneously by an all-optical dynamic decoupling approach based on Raman scattering in the 87Rb Zeeman sublevels. By adjusting the parameters of the Raman lasers, we realize spin control along an arbitrary direction. We analyze the state evolution of atomic spin under the Raman light control sequence in detail. The results show that both the nonlinear Zeeman effect and magnetic field gradient can be significantly suppressed.

A nonlinear phase shift is introduced to a Mach-Zehnder interferometer (MZI), and we present a scheme for enhancing the phase sensitivity. In our scheme, one input port of a standard MZI is injected with a coherent state and the other input port is injected with one mode of a two-mode squeezed-vacuum state. The final interference output of the MZI is detected with the method of active correlation output readout. Based on the optimal splitting ratio of beam splitters, the phase sensitivity can beat the standard quantum limit and approach the quantum Cram\'{e}r-Rao bound. The effects of photon loss on phase sensitivity are discussed. Our scheme can also provide some estimates for units of $\chi^{(3)}$, due to the relation between the nonlinear phase shift and the susceptibility $\chi^{(3)}$ of the Kerr medium., Comment: 4 figures

A new type of atom-light hybrid quantum gyroscope (ALHQG) is proposed due to its high rotation sensitivity. It consists of an optical Sagnac loop to couple rotation rate and an atomic ensemble as quantum beam splitter/recombiner (QBS/C) based on atomic Raman amplification process to realize the splitting and recombination of the optical wave and the atomic spin wave. The rotation sensitivity can be enhanced by the quantum correlation between Sagnac loop and QBS/C. The optimal working condition is investigated to achieve the best sensitivity. The numerical results show that the rotation sensitivity can beat the standard quantum limit (SQL) in ideal condition. Even in the presence of the attenuation under practical condition, the best sensitivity of the ALHQG can still beat the SQL and is better than that of a fiber optic gyroscope (FOG). Such an ALHQG could be practically applied for modern inertial navigation system., Comment: 5 figures

We theoretically study the angular displacements estimation based on a modified Mach-Zehnder interferometer (MZI), in which two optical parametric amplifiers (PAs) are introduced into two arms of the standard MZI, respectively. The employment of PAs can both squeeze the shot noise and amplify the photon number inside the interferometer. When the unknown angular displacements are introduced to both arms, we derive the multiparameter quantum Cram\'er-Rao bound (QCRB) using the quantum Fisher information matrix approach, and the bound of angular displacements difference between the two arms is compared with the sensitivity of angular displacement using the intensity detection. On the other hand, in the case where the unknown angular displacement is in only one arm, we give the sensitivity of angular displacement using the method of homodyne detection. It can surpass the standard quantum limit (SQL) and approach the single parameter QCRB. Finally, the effect of photon losses on sensitivity is discussed.

A novel two-mode non-degenerate squeezed light is generated based on a four-wave mixing (4WM) process driven by two pump fields crossing at a small angle. By exchanging the roles of the pump beams and the probe and conjugate beams, we have demonstrated the frequency-degenerate two-mode squeezed light with separated spatial patterns. Different from a 4WM process driven by one pump field, the refractive index of the corresponding probe field $n_{p}$ can be converted to a value that is greater than $1$ or less than $1$ by an angle adjustment. In the new region with $n_{p}<1$, the bandwidth of the gain is relatively large due to the slow change in the refractive index with the two-photon detuning. As the bandwidth is important for the practical application of a quantum memory, the wide-bandwidth intensity-squeezed light fields provide new prospects for quantum memories.

Strain-coupled magnetoelectric (ME) phenomena in piezoelectric / ferromagnetic thin-film bilayers are a promising paradigm for sensors and information storage devices, where strain is utilized to manipulate the magnetization of the ferromagnetic film. In-plane magnetization rotation with an electric field across the film thickness has been challenging due to the virtual elimination of in-plane piezoelectric strain by substrate clamping, and to the requirement of anisotropic in-plane strain in two-terminal devices. We have overcome both of these limitations by fabricating lithographically patterned devices with a piezoelectric membrane on a soft substrate platform, in which in-plane strain is freely generated, and a patterned edge constraint that transforms the nominally isotropic piezoelectric strain into the required uniaxial strain. We fabricated 500 nm thick, (001) oriented [Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$]$_{0.7}$-[PbTiO$_3$]$_{0.3}$ (PMN-PT) unclamped piezoelectric membranes with ferromagnetic Ni overlayers. Guided by analytical and numerical continuum elastic calculations, we designed and fabricated two-terminal devices exhibiting Ni magnetization rotation in response to an electric field across the PMN-PT. Similar membrane heterostructures could be used to apply designed strain patterns to many other materials systems to control properties such as superconductivity, band topology, conductivity, and optical response.

We theoretically study the quantum Fisher information (QFI) of the SU(1,1) interferometer with phase shifts in two arms taking account of realistic noise effects. A generalized phase transform including the phase diffusion effect is presented by the purification process. Based on this transform, the analytical QFI and the bound to the quantum precision are derived when considering the effects of phase diffusion and photon losses simultaneously. To beat the standard quantum limit with the reduced precision of phase estimation due to noisy, the upper bounds of decoherence coefficients as a function of total mean photon number are given., Comment: 9 pages, 5 figures

Quantum memories with high efficiency and fidelity are essential for long-distance quantum communication and information processing. Techniques have been developed for quantum memories based on atomic ensembles. The atomic memories relying on the atom-light resonant interaction usually suffer from the limitations of narrow bandwidth. The far-off-resonant Raman process has been considered a potential candidate for use in atomic memories with large bandwidths and high speeds. However, to date, the low memory efficiency remains an unsolved bottleneck. Here, we demonstrate a high-performance atomic Raman memory in Rb87 vapour with the development of an optimal control technique. A memory efficiency of 82.6% for 10-ns optical pulses is achieved and is the highest realized to date in atomic Raman memories. In particular, an unconditional fidelity of up to 98.0%, significantly exceeding the no-cloning limit, is obtained with the tomography reconstruction for a single-photon level coherent input. Our work marks an important advance of atomic Raman memory towards practical applications in quantum information processing., Comment: 6 pages, 3 figures

Enhanced Raman scattering can be obtained by injecting a seeded light field which is correlated with the initially prepared collective atomic excitation. This Raman amplification process can be used to realize atom-light hybrid interferometer. We numerically calculate the phase sensitivities and the signal-to-noise ratios of this interferometer with the method of homodyne detection and intensity detection, and give their differences between this two methods. In the presence of loss of light field and atomic decoherence the measure precision will be reduced which can be explained by the break of the intermode decorrelation conditions of output modes, Comment: 9 pages, 7 figures

Charged polar interfaces such as charged ferroelectric domain walls or heterostructured interfaces of ZnO/(Zn,Mg)O and LaAlO3/SrTiO3, across which the normal component of electric polarization changes suddenly, can host large two-dimensional conduction. Charged ferroelectric walls, which are energetically unfavorable in general, were found to be mysteriously abundant in hybrid improper ferroelectric (Ca,Sr)3Ti2O7 crystals. From the exploration of antiphase boundaries in bilayer-perovskites, we discover that each of four polarization-direction states is degenerated with two antiphase domains, and these eight structural variants form a Z4xZ2 domain structure with Z3 vortices and five distinct types of domain walls, whose topology is directly relevant to the presence of abundant charged walls. We also discover a zipper-like nature of antiphase boundaries; they are the reversible creation/annihilation centers of pairs of two types of ferroelectric walls (and also Z3-vortex pairs) in 90 and 180 degree polarization switching. Our results demonstrate the unexpectedly rich nature of hybrid improper ferroelectricity.

Coherent wave splitting is crucial in interferometers. Normally, the waves after this splitting are of the same type. But recent progress in interaction between atom and light has led to the coherent conversion of photon to atomic excitation. This makes it possible to split an incoming light wave into a coherent superposition state of atom and light and paves the way for an interferometer made of different types of waves. Here we report on a Rabi-like coherent-superposition oscillation observed between atom and light and a coherent mixing of light wave with excited atomic spin wave in a Raman process. We construct a new kind of hybrid interferometer based on the atom-light coherent superposition state. Interference fringes are observed in both optical output intensity and atomic output in terms of the atomic spin wave strength when we scan either or both of the optical and atomic phases. Such a hybrid interferometer can be used to interrogate atomic states by optical detection and will find its applications in precision measurement and quantum control of atoms and light.

The quantum correlation of light and atomic collective excitation can be used to compose an SU(1,1)-type hybrid light-atom interferometer, where one arm in optical SU(1,1) interferometer is replaced by the atomic collective excitation. The phase-sensing probes include not only the photon field but also the atomic collective excitation inside the interferometer. For a coherent squeezed state as the phase-sensing field, the phase sensitivity can approach the Heisenberg limit under the optimal conditions. We also study the effects of the loss of light field and the dephasing of atomic excitation on the phase sensitivity. Since nonlinear processes are involved in this interferometer, they can couple a variety of different waves and form new types of hybrid interferometers, which provides a new method for basic measurement using the hybrid interferometers., Comment: 6 pages

We theoretically propose a method to enhance Raman scattering by injecting a seeded light field which is correlated with the initially prepared atomic spin wave. Such a light-atom correlation leads to an interference in the Raman scattering. The interference is sensitive to the relative phase between the seeded light field and initially prepared atomic spin wave. For constructive interference, the Raman scattering is greatly enhanced. Such an enhanced Raman scattering may find applications in quantum information, nonlinear optics and optical metrology due to its simplicity., Comment: 5 pages, 4 figures

We experimentally demonstrate efficient Raman conversion to respective Stokes and anti-Stokes fields in both pulsed and continuous modes with a Rb-87 atomic vapor cell. The conversion efficiency is about 40-50% for the Stokes field and 20-30% for the anti-Stokes field, respectively. This conversion process is realized with feedback of both the Raman pump and the frequency-converted fields (Stokes or anti-Stokes). The experimental setup is very simple and can be applied easily to produce the light source with larger frequency difference using other Raman media. They may have wide applications in nonlinear optics, atomic physics, quantum optics and precise measurement., Comment: 4 pages, 5 figure

We present a scheme to generate the frequency multiplexed entangled (FME) single photons based on the entanglement between two species atomic mixture ensemble. The write and reads fields driven according to a certain timing sequence, the generation of FME single photons can be repeated until success is achieved. The source might have significant applications in wavelength division multiplexing quantum key distribution., Comment: 4 pages, 4 figures, submitted to PRA

We present a scheme to obtain the coherently enhanced Raman scattering in atomic vapor which is induced by a spin wave initially written by a weak write laser. The enhancement of Raman scattering is dependent on the number and the spatial distribution of the flipped atoms generated by the weak write laser. Such an enhanced Raman scattering may have practical applications in quantum information, nonlinear optics and laser spectroscopy because of its simplicity., Comment: 7 pages, 4 figures, submitted to Phys. Rev. A

Coherent conversion between a Raman pump field and its Stokes field is observed in a Raman process with a strong atomic spin wave initially prepared by another Raman process operated in the stimulated emission regime. The oscillatory behavior resembles the Rabi oscillation in atomic population in a two-level atomic system driven by a strong light field. The Rabi-like oscillation frequency is found to be related to the strength of the pre-built atomic spin wave. High conversion efficiency of 40% from the Raman pump field to the Stokes field is recorded and it is independent of the input Raman pump field. This process can act as a photon frequency multiplexer and may find wide applications in quantum information science.

Domain wall dynamics in ferroic materials underpins functionality of data storage and information technology devices. Using localized electric field of a scanning probe microscopy tip, we experimentally demonstrate a surprisingly rich range of polarization reversal behaviors in the vicinity of the initially flat 180\deg ferroelectric domain wall. The nucleation bias is found to increase by an order of magnitude from a 2D nucleus at the wall to 3D nucleus in the bulk. The wall is thus significantly ferroelectrically softer than the bulk. The wall profoundly affects switching on length scales of the order of micrometers. The mechanism of correlated switching is analyzed using analytical theory and phase-field modeling. The long-range effect is ascribed to wall bending under the influence of a tip bias well below the bulk nucleation field and placed many micrometers away from the wall. These studies provide an experimental link between the macroscopic and mesoscopic physics of domain walls and atomistic models of nucleation., Comment: 52 pages, 8 figures, 2 appendices, to be submitted to Phys. Rev. B, higher quality figures are available upon request

We propose a first-principles formulism for system with spin fluctuations and apply it to the ordered Fe3Pt to uncover the Invar anomalies, including negative thermal expansion and spontaneous magnetization. The theory has coherently predicted the finite temperature intermixing between the fully ferromagnetic configuration and the spin-flipping configurations. We also discover a tri-critical point at which a high-temperature second-order phase transition, between the fully ferromagnetic configuration and the spin-flipping configurations, becomes first-order at low temperatures., Comment: Rephased title and abstract; Reploted figures; Reordered references

Thermodynamic flunctuations in BaFe2As2 is addressed with a first-principles formulation of the Helmholtz energy by accounting for the mixture of various electronic states each distinguished by different spin orientation distributions. We find that it is the spin exchange coupling in the inter-plane c direction that dictates the spin density wave ordering. We quantitatively predicted the pressure dependence of the spin density wave ordering, the Schottky anomaly, and the temperature dependence of thermal populations of spin structures, all in agreement with available experimental data.

Multiferroicity can be induced in strontium titanate by applying biaxial strain, resulting in the coexistence of both ferroelectric and antiferrodistortive domains. The magnitude and sign of the strain imposed on the lattice by design can be used to tune the phase transitions and interactions between these two phenomena. Using optical second harmonic generation, we report a transition from centrosymmetric 4/mmm phase to ferroelectric mm2, followed by an antiferrodistortive transition to a coupled ferroelastic-ferroelectric mm2 phase in a strontium titanate thin film strained in biaxial tension by 0.94%. The results agree well with theoretical first principles and phase-field predictions. Direct imaging of domains arising from the ferroelectric phase transition, and its switching under electric fields is demonstrated using piezoelectric force microscopy. Nonlinear optics combined with phase-field modeling is used to show that the dominant multiferroic domain switching mechanism is through coupled 90 degree ferroelectric-ferroelastic domain wall motion. More broadly, these studies of coexisting ferroelectric (polar) and antiferrodistortive rotation (axial) phenomena could have relevance to multiferroics with coexisting ferroelectric (polar) and magnetic (axial) phenomena., Comment: 5 pages, 4 figures, In review in Physical Review Letters