Pump Probe Spectroscopy
Pump probe spectroscopy is the simplest experimental technique used to study ultrafast electronic dynamics. In this technique, an ultrashort laser pulse is split into two portions; a stronger beam (pump) is used to excite the sample, generating a non-equilibrium state, and a weaker beam (probe) is used to monitor the pump-induced changes in the optical constants (such as reflectivity or transmission) of the sample. Measuring the changes in the optical constants as a function of time delay between the arrival of pump and probe pulses yields information about the relaxation of electronic states in the sample.
Transient Grating Spectroscopy
Pump probe spectroscopy described above is well suited for measuring the lifetime of electronic excitations with femtosecond time resolution. In order to measure propagation of these excitations in real space, we use transient grating spectroscopy. In this technique, a pair of femtosecond pulses is interfered on the sample to generate a sinusoidal intensity modulation, that in turn induces a density grating of photoexcitations. Because the index of refraction depends on the local excitation density, a periodic modulation of the index of refraction is formed. The period of this pattern in real space can be changed either by changing the wavelength of the laser or the angle between the two beams. An incident probe pulse on this pattern is therefore both reflected and diffracted. Measuring the time evolution of both the reflected and diffracted waves enables us to track the propagation of these excitations in real space.
Circular Dichroism and Time-Resolved ARPES
Angle resolved photoemission spectroscopy (ARPES) is a powerful tool for mapping the electronic bandstructure of solids by measuring the energy and momentum of photoemitted electrons. In our lab we use UV laser pulses and a time-of-flight spectrometer (shown on the left), which simultaneously measures the photoemitted electron energy by its flight time, and momentum Kx and Ky using a 2D position-sensitive-detector. As a result, 3D intensity spectra I(E,Kx,Ky) (shown on the right for the topological insulator Bi2Se3) are obtained.
We can also look for circular dichroism, which is the difference in the ARPES intensity spectrum obtained with right- vs. left-circularly polarized light. In some materials, such as the topological insulator Bi2Se3, this can be a sensitive measure of the electron spin orientation in momentum space (below left). The ultrafast dynamics of electrons can also be resolved by performing ARPES in a pump-probe scheme. An 80 fs ultrafast laser pulse pumps the sample to initiate electronic excitation and the excited system is then probed by the delayed UV pulse that photoemits electrons for the ARPES measurement. By sweeping the delay time t between the two pulses while collecting the 3D intensity spectra I(E,Kx,Ky), we obtain a 3D movie of I(E,Kx,Ky,t) that captures electronsí dynamics in the solids on femtosecond time scale (below right for Bi2Se3).
Second Harmonic Generation
A technique our lab has been researching to gain exclusive sensitivity to the surface of a material is optical second harmonic geneartion (SHG). In general, the electrical polarization of a material Pi(ω) has a dominant component linear in the driving optical field Ej(ω) as well as weaker components proportional to higher powers of Ej(ω), where ω is the optical frequency and the indices run through three spatial coordinates. Components that contain two powers of Ej(ω) are responsible for SHG. For electric dipole processes, the polarization Pi = χ(2)ijkEjEk is obtained from a third rank susceptibility tensor χ(2)ijk that vanishes under inversion symmetry. Therefore dipole induced SHG is forbidden in bulk crystals with inversion symmetry and is only allowed at surfaces or interfaces where inversion symmetry is necessarily broken. By measuring the reflected output as the sample is rotated about its surface normal axis, we obtain patterns like those shown below for Bi2Se3, which reveal the symmetry of the surface electronic polarizability.
The ultrafast pulsed nature of the laser light used to perform SHG naturally lends itself to the study of ultrafast dynamics on the surface of materials. In these types of experiment, a pulse of laser light (pump) is first impinged onto the sample in order to create a non-equilibrium electron distribution. A second time delayed pulse (probe) is then used to monitor the temporal evolution of the SHG signal (see below). The relaxation dynamics of the non-equilibrium distribution can be used to understand the microscopic energy loss mechanisms of the surface electrons.
TeraHertz Time-Domain Spectroscopy
Terahertz Time-Domain Spectroscopy (THz-TDS) is an optical technique used to measure equilibrium and non-equilibrium far infrared material properties such as index of refraction and conductivity. A THz pulse is generated via optical rectification in a ZnTe crystal using a 100 fs near-infrared pulse. The THz pulse is then focused through a sample and subsequently detected in another ZnTe crystal via free space electro-optic detection. The measured signal is proportional to the electric field of the pulse, so the magnitude and phase are preserved, and the complex transmission coefficient can be extracted. From this, the full complex value of the material parameters can be extracted without the use of Kramers-Kronig relations.
This can also be done after excitation by another 100 fs near-infrared pulse. By varying the time delay between the THz pulse and the excitation pulse, the non-equilibrium complex material parameters can be measured as a function of time, with resolution < 500 fs.
THz-TDS is best used to study systems in which the excitations of interest lie in the meV energy range, e.g., a superconductor with a small energy gap. The technique has been used to study a wide variety of systems, including Cooper pair and vortex dynamics in superconductors, carrier dynamics in semiconductors, metal-insulator phase transitions, and even metamaterials.
Ultrafast Electron Diffraction
Direct determination of structural dynamics requires the ability of measuring atomic motions with angstrom scale spatial resolution. Conventional ultrafast optical spectroscopy based on measuring transient changes in optical constants is sensitive to dynamics of electronic excitations but can provide only indirect information about structural dynamics. The spatial resolution in these techniques is also limited to micron scales due to diffraction limit.
Ultrafast electron diffraction (UED) can directly couple to structural dynamics and provide sub-angstrom spatial resolution together with sub-picosecond temporal resolution. The principle of UED is similar to pump probe spectroscopy. An ultrafast laser pulse is split into two; the first part of the laser pulse is directly focused on to the sample to create a non-equilibrium state. To probe the induced structural change, the second part is frequency tripled and focused on to a photocathode generating an ultrafast electron packet via photoelectric effect. These electrons are then accelerated through a high voltage (typically through 30 keV, de Broglie wavelength = 0.07 Å) and diffracted from the sample.
The relative arrival time of the probing electron packet and the initiating laser pulse at the sample can be changed by changing the relative optical path-lengths of the two laser beams. Recording the diffraction pattern of the electron packet as a function of this time delay provides both the equilibrium structure and a movie of the structural evolution with sub-Angstrom spatial resolution (reaching ~0.001 Ň level) and sub-picosecond temporal resolution.
The topological insulator is a fundamentally new phase of electronic matter that defies the conventional Landau symmetry breaking paradigm. They are realized in electrically insulating materials whose band gap is induced by large spin-orbit coupling. One of the unique and defining characteristics of a topological insulator is the presence of spin-polarized metallic surface states that obey a light-like dispersion relation (see left).
These surface states have recently been proposed to be a platform for realizing exotic particles such as Majorana fermions as well as realizing optical and spintronic devices with new functionalities.
In our lab we are investigating the optical properties of the surface states of topological insulators. This is a challenging task because the surface states are confined to an ultra narrow nanometer region of the surface whereas probe photons penetrate much deeper into the material. Therefore the surface state contribution to any optical signal is typically only a tiny addition to a predominantly bulk response.
Iridium oxides are unique 5d electronic systems in which spin-orbit coupling, electronic bandwidth and on-site Coulomb interactions occur on comparable energy scales. Their interplay can stabilize a novel spin-orbital entangled Jeff = 1/2 Mott insulating state in which a correlation gap is opened by only moderate Coulomb interactions owing to a spin-orbit coupling induced band narrowing.
Below a critical temperature TN the localized Jeff = 1/2 moments undergo long-range ordering. However owing to an absence of clear anomalies at TN in transport, thermodynamic and optical conductivity data, there have been conflicting interpretations about how the insulating gap behaves across TN. We use time-resolved optical spectroscopy, which is highly sensitive to the existence of energy gaps, to study the temperature evolution of the electronic structure of Sr2IrO4. Taking advantage of qualitatively distinct relaxation dynamics of photo-excited carriers exhibited by gapped and gapless systems, we find a clear change in the ultrafast dynamics across TN indicating a gap opening concomitant with antiferromagnetic order.
Superconductivity is the result of the resistanceless flow of paired electrons known as Cooper pairs. In conventional materials, such as pure metals and alloys, the cause of this phenomenon is well known: a distortion of the lattice, produced by the passage of one electron, serves to attract a second electron in its wake. By contrast, the mechanism of high temperature superconductivity, exhibited separately by the copper oxide and iron pnictide superconductors, has yet to be successfully understood. What binds these electrons together? Are copper oxide and iron pnictide superconductivity related? How do the various other forms of electronic order exhibited by both classes, such as antiferromagnetism in the cuprates and spin-density wave order in the pnictides, impact superconductivity?
We have been attempting to address these fundamental questions using the powerful methods of ultrafast time-resolved spectroscopies. In these measurements, we break the Cooper pair apart using a femtosecond laser pulse. By watching the dynamics of these particles in real time as they relax and recreate their original ordered state, we can learn about how these charge carriers organize themselves within the solid, gain insight into what glues them together into Cooper pairs, and how superconductivity interacts with the other coexisting forms of order.
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