SUPPLEMENTARY INFORMATION

Transcription

1 SUPPLEMENTARY INFORMATION doi: /nature Supplementary Methods The three QW samples on which data are reported in the Letter (15 nm) 19 and supplementary materials (18 and 22 nm) 23 were grown by molecular beam epitaxy. They consist of 10 repetitions of 15/18/22 nm In 0.06 Ga 0.94 As quantum wells between 30 nm Al 0.3 Ga 0.7 As barriers 31. The NIR polarization is parallel to the THz polarization unless otherwise noted. The sidebands are measured using an SPEX m dual grating spectrometer and a Hamamatsu R74000U-20 photomultiplier tube. An Edmund optics OD4 short pass filter is used to prevent non-laser emission from the Titanium-Sapphire laser from adding to the background noise detected in the monochromator. The slits on the monochromator are set so that the resolution is ~0.2 mev (~0.1 nm). The signal from the photomultiplier tube is sent through two stages of an SRS SR445 DC-300MHz amplifier to generate a gain of 25. The sidebands are then measured by either an oscilloscope or an SRS SR400 two channel gated photon counter depending on the strength of the sideband. The repetition rate of the FEL is quite low (<1 Hz) and measurements are taken with 10 averages. To produce graphs of the full spectrum, a few sidebands are measured using both the oscilloscope and photon counter and the relative magnitudes of these signals are used to properly scale the amplitudes of the rest of the sidebands. Signals measured with an oscilloscope have a background which is limited by electrical noise and the resolution of the scope. When the signal is measured using the photon counter, the background is limited by stray light which causes false counts. The average number of false counts per measurement is less than one, so the total number of counts measured when not measuring a sideband is often zero. However, to properly express the signal to noise ratio of our experiment, the amplitude of the signal used in the figures at these points is non-zero and is representative of the rate of false counts as compared to the actual measured signal. The errors quoted from data measured with an oscilloscope are given as a standard error of the mean. The errors quoted when measurements are taken with the photon counter are given by the square root of the number of counts, as typical for photon counting statistics. In the experiments performed, the UCSB free electron lasers (FELs) are the source of the tunable, high intensity THz radiation. The electric field is estimated from the power during the FEL pulse and the spot size of the focused THz beam. The spot size is estimated from measurements using a Spiricon imaging system. The spot is taken to have a radius of 0.5±0.05 mm at a frequency of 0.58 THz. In order to produce the most intense electric fields, pulses of 40 ns are created by cavity dumping 32 the FEL. The energy in each FEL pulse is measured by a Laser Precision Corp. RJ-7620 energy ratiometer and is used to estimate the power. The maximum energy available at the sample is greater than 100 µj per pulse at 0.58 THz. The electric field can then be calculated,, where F is the field, P is the power at the sample, A is the area of the THz spot and n is the refractive index in the material, taken to be 3.3 in the sample. The uncertainties quoted for the electric fields are due to fluctuations in the FEL power and uncertainty in the size of the THz spot. To estimate the electric fields currently available from on-chip terahertz transistor amplifiers we assume an available power of 10mW at a frequency of 300 GHz 30. Using a transmission line such as a coplanar waveguide with a resistance of 50Ω and a gap on the order of a micron, we can estimate the electric field available: 1

2 RESEARCH SUPPLEMENTARY INFORMATION Thus, field values that can be achieved from solid-state devices in the extreme near field are comparable to those used in the experiments presented. 2. Supplementary Discussion We can estimate the density of excitons in each QW, ρ exciton, from the NIR power incident on the sample, P NIR = 20 mw, the absorption per QW, α = 0.05, the exciton lifetime, τ < 5 ns, the NIR spot size r = 250 µm and the NIR photon energy Ω NIR. The density will then be given by From this we estimate the inter-excitonic spacing to be greater than 100 nm at the highest powers. The Bohr radius of the exciton is estimated to be ~10 nm using a relative permittivity of ε ~ 13 and an effective mass m eff * ~ m e. Thus, in these experiments we are not approaching the Mott density where excitons overlap. Given the low density of excitons, an electron from a particular exciton can reasonably be expected to be ionized, accelerated away from the hole to which it was bound, and recollide with that same hole without scattering off of another one. We note that the ~10 mev binding energy of the exciton is ~4-5 times the THz photon energy for 1.9 and 2.4 mev photons at 0.46 and 0.58 THz, respectively. This energy barrier is enough to prevent single or two photon ionization of the exciton. As is necessary for the recollision model, we assume that multiphoton ionization can be approximated as a tunneling phenomenon 14. The photon energies at these frequencies are also small enough to be far from the excitonic 1s-2p transition energy. Previous work has shown that intense THz beams can heat unbound electrons and holes created by photon energies well above the band gap, observed by quenching of the (incoherent) photoluminescence 33. In contrast, HSG is robust and there is no indication that heating of unbound electrons and holes influence our results. Here, since we are resonantly creating excitons, the only unbound electron hole pairs present should be excitons ionized by the THz field. We suspect that we are ionizing a sufficiently small population to avoid observing any effects in our measurements. 3. Supplementary Data The effect of HSG was consistent throughout multiple QW samples investigated. Supplemental Fig. S1 shows the HSG spectra of quantum wells with 15 nm and 18 nm widths 23 with an intense 0.58 THz applied electric field. When the NIR laser frequency is adjusted to properly match the frequency of exciton formation for each sample, the HSG phenomenon is observed and the number of high order sidebands is consistent between the samples. Temperature dependent measurements of the +6f FEL, +8f FEL, and +10f FEL sidebands are shown in Supplemental Fig. S2. Though a systematic dependence of the sideband intensity on temperature is not 2

3 SUPPLEMENTARY INFORMATION RESEARCH established from these measurements, we do observe sideband generation up to 100K. We find that there is a maximum in the sideband intensity at 80K. We attribute this increase in the sideband signal to the temperature induced red-shift of the band gap which tunes the exciton transition slightly closer to resonance with the NIR laser and slightly enhances the sideband generation. We would like to point out that we have not adjusted the NIR laser to match the shift of the band gap and exciton resonance. It may be the case that our decrease in signal at higher temperatures is due to this detuning of the exciton resonance from the NIR laser and not solely from a temperature dependent change in the sideband generation efficiency, implying that sidebands may be present above 100K. At NIR frequencies significantly detuned above or below the exciton line there is no sideband generation observed. Near infrared laser spectra from a 22 nm QW sample 23 at a number of NIR frequencies are shown in Supplemental Fig. S3. The data is taken with a m spectrograph and an intensified CCD array (ICCD). This setup allows for increased data throughput at the cost of lower quantum efficiency and higher detector noise. Additionally, signal at the NIR laser frequency blooms into pixels away from the NIR laser line, resulting in a large background at sideband frequencies and limiting the NIR power we can apply to the sample while still measuring the sidebands. Only the +2f FEL sideband is observed. As the NIR laser is detuned from the exciton resonance, the intensity of this sideband quickly decreases. Theory predicts sideband generation and a sideband plateau even when the NIR laser is creating unbound electrons and holes. However, the decrease of the sideband signal by orders of magnitude as the NIR laser is detuned from the exciton resonance indicates a strong excitonic influence on the experimental results 12. Though the sidebands at frequencies above the NIR laser frequency are shown to have a non-perturbative origin, we believe the sidebands at frequencies below the NIR laser frequency are generated perturbatively. For these lower frequency sidebands, there is no plateau region and the sidebands die off rapidly with increasing order. Further support is provided by the quadratic dependence of the 2 nd order negative sideband on the FEL intensity, shown in Supplemental Fig. S4. Sideband generation at a number of NIR powers is shown for multiple sidebands in Supplemental Fig. S5. For fixed THz field amplitude (FEL intensity), the intensity of all sidebands increases linearly with NIR power at the lowest NIR powers used. The sideband intensities increase sub-linearly with NIR power at the highest NIR powers used. For the +2f FEL sideband, the dependence of sideband intensity on NIR power is the same, up to a scale factor, for both relatively low THz field amplitudes and for the highest THz field amplitudes, at which the dependence of sideband intensity on THz field is saturated. 4. Supplementary Equations The dependence of the sideband generation on the ellipticity of the THz polarization can be written to lowest order by symmetry arguments. The electric field is given by where and, and and are the amplitudes of circular and counter-circular polarized THz fields, respectively. Due to the symmetry of the system, the total angular momentum of the 3

4 RESEARCH SUPPLEMENTARY INFORMATION photons absorbed must be 0. Generation of the n th sideband requires absorption of n pairs of circular and counter-circular polarized photons to conserve angular momentum, leading to a polarization in the sample This leads to a dependence of the sideband intensity on the phase which describes the ellipticity of the THz polarization. For comparison, this dependence is plotted (chained line) with the experimental data in Fig. 3 and shows very good agreement with the sidebands measured. 5. Supplementary Figures and Legends Figure S1: High-order sideband generation in quantum well samples with different widths. The NIR laser frequency was shifted to match the exciton energy in each sample. In both samples, sideband emission up to 18 th order was observed, and the relative amplitudes of the sidebands are similar, indicating that high-order sideband generation is robust to changes in well width. Error bars represent standard errors of the mean (s.e.m.). 4

5 SUPPLEMENTARY INFORMATION RESEARCH Figure S2: Temperature dependent data of the 3 rd, 4 th and 5 th sidebands in a 15 nm QW with f FEL = 0.58 THz. The sidebands are observed up to 100 K. 5

6 RESEARCH SUPPLEMENTARY INFORMATION Figure S3: Near infrared frequency dependence of the sideband generation in a 22 nm QW driven by a 0.48 THz field. The +2f FEL sideband (black arrows) is observed when the NIR is resonant with the exciton transition. As the NIR is detuned from the exciton resonance, the sideband intensity decreases and the sideband signal is undetectable by the ICCD. 6

7 SUPPLEMENTARY INFORMATION RESEARCH Figure S4: The dependence of the intensity of the first sideband below the NIR laser line on FEL intensity in a 15 nm QW with f FEL = 0.58 THz. The data is well modeled by an I 2 fit, implying the perturbative nature of the sideband generation. Error bars represent s.e.m. 7

8 RESEARCH SUPPLEMENTARY INFORMATION Figure S5: In a 22 nm QW driven by a 0.58 THz field, the dependence of the sideband strength on the NIR power is similar for all sidebands measured. The sideband strength increases linearly at lower NIR powers and increases sublinearly at the highest NIR powers. Graph a) shows NIR power dependence for both second order sidebands normalized to ~1 at the maximum sideband power. Graph b) shows the NIR power dependence of the second-order positive sideband at and below THz saturation (normalized). Graphs c) and d) show the NIR power dependence of the 4 th and 6 th order sidebands, respectively. Error bars represent s.e.m. References 31 Carter, S. G. Terahertz electro-optic effects in (In)GaAs quantum wells, Ph.D. Thesis, University of California at Santa Barbara, (2004). 32 Kaminski, J. P. et al. Far-infrared cavity dump coupling of the UC Santa Barbara free-electron laser. App. Phys. Lett. 57, (1990). 33 Černe, J. et al. Quenching of excitonic quantum-well photoluminescence by intense far-infrared radiation: Free-carrier heating. Phys. Rev. B 51, (1995). 8