Photon storage with sub-nanosecond readout rise time in coupled quantum wells
PPhoton storage with sub-nanosecond readout rise time in coupled quantumwells
A.G. Winbow, L.V. Butov, and A.C. Gossard Department of Physics, University of California at San Diego, La Jolla, CA 92093-0319 Materials Department, University of California at Santa Barbara,Santa Barbara, California 93106-5050 (Dated: July 11, 2008)
Abstract
The following article has been accepted by Journal of Applied Physics. After it is published, it will befound at http://jap.aip.org/
Photon storage with 250 ps rise time of the readout optical signal was implemented with indirect excitonsin coupled quantum well nanostructures (CQW). The storage and release of photons was controlled bythe gate voltage pulse. The transient processes in the CQW were studied by measuring the kinetics ofthe exciton emission spectra after application of the gate voltage pulse. Strong oscillations of the excitonemission wavelength were observed in the transient regime when the gate voltage pulse was carried overan ordinary wire. Gating the CQW via an impedance-matched broadband transmission line has lead toan e ff ective elimination of these transient oscillations and expedient switching of the exciton energy to arequired value within a short time, much shorter than the exciton lifetime. a r X i v : . [ c ond - m a t . m e s - h a ll ] J u l hoton storage is an essential part of optical signal processing in optical networks. E ffi cientphoton storage in semiconductor nanostructures has been recently demonstrated. Photons werestored in the form of separated electrons and holes in acoustically and electrostatically induced lateral superlattices, quantum dot pairs, and coupled quantum wells (CQW). The fastest demonstrated rise time of the readout optical signal in these devices was about onenanosecond.
Here, we report on refining the photon storage in CQW and achieving a 250 psrise time of the readout optical signal. The refining also has led to an e ff ective elimination oftransient oscillations after the storage pulse.The storage device employs spatially separated electrons and holes in CQW, Fig. 1a. The samedevice was employed in the proof of principle photon storage in CQW. The storage is presentedfor low temperatures where the spatially separated electrons and holes are bound, forming indi-rect excitons (for a review on indirect excitons see Ref. 13); however, the operation principle ofthe device is the same at high temperatures for unbound electrons and holes. The same deviceand temperature as in Ref. 11 are studied in this paper so that the refined photon storage can becompared with the earlier one.The principle of the photon storage with CQW is as follows: The emission rate of the indi-rect excitons (or unbound electrons and holes) is determined by the overlap between the electronand hole wave functions and can be controlled by the applied gate voltage, typically within sev-eral orders of magnitude. The energy of the indirect excitons (or unbound pair of electron andhole) is also controlled by the applied gate voltage V g , which results in the exciton energy shift δ E = edF z , where d is the separation between the electron and hole layers (close to the distancebetween the QW centers), F z = V g / D is an electric field perpendicular to the QW plane, and D isthe width of the intrinsic layer in the n + − i − n + CQW sample. The energy can be typically con-trolled within several tens of meV in CQW samples. Figs. 2a-d present the schematic of the photonstorage. Photons generated by a laser pulse (Fig. 2a) are absorbed in the CQW device. Writingis performed by the gate voltage pulse V g (Fig. 2b), which reduces the exciton emission rate andstores the absorbed photons in the form of indirect excitons. Emission of the indirect excitonsduring storage occurs at energy lower by approximately edV g / D (for corrections due to the inter-action see Ref. 13) and is weak due to their long lifetimes. This emission is shown schematically inFig. 2d. Readout of the stored photons is provided by termination of the gate voltage pulse, whichincreases the emission rate and results in conversion of excitons back to photons (Fig. 2c). Theearlier implementation of this scheme demonstrated photon storage with microsecond storage2ime and nanosecond rise time of the optical readout.A principal limitation of the proof-of-principle experimental setup was that the gate voltagepulse from the pulse generator was delivered to the CQW sample via ordinary wires over ∼ ∼ c / f is smaller than the ∼ Z = Ω , while theCQW sample has resistance between the top and bottom planes in the range of M Ω - G Ω dependingon the laser excitation and acts approximately as a parallel plate capacitor with C ∼ (cid:15) S / π D ∼
60 pF, where S ∼ . × . is the sample area. (Note that such circuit also acts as an RC low-pass filter, which slows the switching time.) The apparent impedance mismatch between theordinary wire and the sample results in reflection of the voltage pulse at the sample and oscillationof the applied voltage V g and electric field F z = V g / D in the sample. We detected these oscillationsby analysis of the evolution of the emission spectra, as described below. (The voltage oscillationswere also observed on an oscilloscope.) These oscillations hinder the storage in two ways: First,each swing of the oscillating electric field reduces the exciton lifetime and, therefore, reduces thephoton storage e ffi ciency. Second, the oscillations complicate the readout process, while waitingfor their damping (as in the proof-of-principle experiment) sets a minimum storage time.Furthermore, an ordinary wire also acts as an antenna. In the case when multiple gate voltagesare applied to the CQW sample via di ff erent wires, the radiation emitted by such an antenna canlead to crosstalk among the wires. Multiple wires are used for creating potential landscapes forexcitons, as discussed below, and thus eliminating crosstalk is required for improving the controlof potential landscapes for excitons.Therefore, improving the device performance requires gating the CQW via an impedance-matched broadband transmission line appropriate for the demanded switching speed. In this paper,we exploit gating the CQW sample via a broadband coaxial cable with a 50 Ω termination resistor,see Fig. 1b. This method can be applied to a variety of semiconductor structures of diverse layerdesigns. The achieved performance improvement of our device is described below. n + − i − n + GaAs / AlGaAs CQW samples were grown by molecular beam epitaxy. The i region con-sists of a single pair of 8 nm GaAs QWs separated by a 4 nm Al . Ga . As barrier and surrounded3y 200 nm Al . Ga . As barrier layers. The n + layers are Si-doped GaAs with N Si = × cm − .The electric field in the sample growth direction F z is controlled by the gate voltage V g appliedbetween n + layers. At V g =
0, the lowest energy state in the CQW is the direct exciton with a shortlifetime, while at V g ∼ . µ s for the studied sample.The carriers were photoexcited by a 635 nm laser diode. The 200 ns laser excitation pulse(Fig. 2a) has a rectangular shape with edge sharpness ∼ . µ W and the excitation spot diameter was ∼ µ m. Theemitted light was di ff racted by a single-grating spectrometer and detected by a Peltier-cooled pho-tomultiplier tube and time correlated photon counting system. The experiments were performedin a He cryostat at T ≈ / fall time. (Note that the rise time of the readout signal was shorterthan 0.5 ns; after termination of the gate voltage pulse, the emission line moves to higher energiesto reach the energy at zero electric field and the rise time of the readout optical signal measuredat this energy depends on the spectral shape of the emission line and is faster for the lines with asharp high-energy edge.) The pulse was transmitted within the cryostat over a semi-rigid coaxialcable UT-141B-SS with silver-plated beryllium-copper inner conductor, PTFE teflon dielectric,and stainless-steel outer shell of diameter 3.6 mm, having room-temperature attenuation of 3 dB / mat 10 GHz. The cable bandwidth complies with the requirement for fast control while the cablecomposition reduces heat conductance to the sample, thus facilitating future measurements withseveral such cables at low temperatures. The cable was routed vertically straight from the samplethrough the exterior vacuum SMA feedthrough and countersunk in a channel in the sample planefor good electrical ground. The 5 mm contact pin from the sample socket passed through a hole inthe ground plane and terminated on the back side with a metal-film surface-mount resistor having50 Ω at 4.2 K.Figure 2f shows that the rise time of the readout optical signal in the refined system was 250 ps,which is an improvement compared to the nanosecond rise time achieved in earlier studies.We also analyzed the transient processes in the CQW after the storage pulse by measuring thekinetics of the exciton emission spectra. Figures 3c,d show the presence of strong oscillations ofthe exciton emission wavelength in the transient regime for the CQW gated via dc-suited wiring.The oscillation of the emission energy E reveals the oscillation of the electric field in the sample4 z , with the relation given by δ E = ed δ F z . After the voltage pulse, the emission wavelength ofthe indirect excitons varies from about 810 nm ( E ≈ .
530 eV) to 793 nm ( E ≈ E ≈ F z ; this causes losses of stored photons.Figures 3a,b show these oscillations are e ff ectively suppressed when the CQW is gated via animpedance-matched broadband transmission line. After application of the gate voltage pulse, theexciton energy changes without oscillations to the value determined by the applied voltage. Thefollowing slow fall in energy observed in Figs. 3a,b is consistent with the reduction of the indirectexciton density with decay, which results in the reduction of the repulsive interaction between theexcitons. The absence of oscillations demonstrates expedient switching at storage. As mentionedabove, the oscillations cause losses of stored photons and complicate the readout processes; theirelimination improves the device performance. Note that the data reported here demonstrate proofof principle for refining the device performance. The issues essential for practical applications,such as device operation at high temperatures, are briefly discussed in Ref. 11.We would like to emphasize an important application of the rapid control of the indirect excitonenergy and lifetime. A laterally modulated gate voltage V g ( x , y ) created by a pattern of electrodeson a sample surface can form a variety of in-plane potential landscapes for indirect excitons inCQW. Particular cases for such potential landscapes include potential gradients, and2D lateral superlattices, traps, and excitonic circuits. The switching of the exciton en-ergy to a required value without oscillations and within a short time, much shorter than the excitonlifetime, Figs. 3a,b, demonstrates an improvement for the control of such potential landscapes,which can be exploited in studying the physics of excitons.Note also that the storage scheme can be used to realize a cold gas of direct excitons. Due totheir short lifetime, direct excitons are typically hotter than the lattice, while indirect excitons livelong enough to cool down essentially to the lattice temperature. In the storage scheme, initiallyhot direct excitons transform to indirect excitons by the voltage pulse, cool down toward the lat-tice temperature during the long storage time, and then transform to direct excitons at the pulsetermination. This method uses the long lifetime of indirect excitons to realize a cold gas of directexcitons after the last step, provided that essentially no heating occurs then. Note that indirectexcitons have a built-in dipole moment and, therefore, interact relatively strongly.
How-ever, direct excitons have no built-in dipole moment and interact weakly. Therefore, this method5ay permit extending the studies of cold exciton gases to a new system of weakly interacting colddirect excitons.In conclusion, gating the CQW via an impedance-matched broadband transmission line haslead to an e ff ective elimination of the transient oscillations in the electric field across the sampleand to expedient switching of the exciton energy to a required value within a short time, muchshorter than the exciton lifetime. A rise time of the readout optical signal as short as 250 ps wasachieved.This work is supported by ARO, DOE, and NSF. We thank K.L. Campman for growing the highquality samples, and R. Heron, G. Kassabian, B. Naberhuis, and R. Parker for help in preparingthe experiment. C. Rocke, S. Zimmermann, A. Wixforth, J. P. Kotthaus, G. B¨ohm, and G. Weimann, Phys. Rev. Lett. ,4099 (1997). P. V. Santos, M. Ramsteiner, and R. Hey, Phys. Stat. Sol. (b) , 253 (1999). S. Zimmermann, A. Wixforth, J. P. Kotthaus, W. Wegscheider, and M. Bichler, Science , 1292 (1999). S. K. Zhang, P. V. Santos, R. Hey, A. Garcia-Cristobal, and A. Cantarero, Appl. Phys. Lett. , 4380(2000). J. Krauß, J. P. Kotthaus, A. Wixforth, M. Hanson, D. C. Driscoll, A. C. Gossard, D. Schuh, and M. Bich-ler, Appl. Phys. Lett. , 5830 (2004). T. Lundstrom, W. Schoenfeld, H. Lee, and P. M. Petro ff , Science , 2312 (1999). M. Kroutvar, Y. Ducommun, J. J. Finley, M. Bichler, G. Abstreiter, and A. Zrenner, Appl. Phys. Lett. , 443 (2003). M. Kroutvar, Y. Ducommun, D. Heiss, M. Bichler, D. Schuh, G. Abstreiter, and J. J. Finley, Nature ,81 (2004). R. J. Young, S. J. Dewhurst, R. M. Stevenson, P. Atkinson, A. J. Bennett, M. B. Ward, K. Cooper, D. A.Ritchie and A. J. Shields, New J. Phys. , 365 (2007). H. J. Krenner, C. E. Pryor, J. He, and P. M. Petro ff , arXiv:0805.1819v1. A. G. Winbow, A. T. Hammack, L. V. Butov, and A. C. Gossard, Nano Lett. , 1349 (2007). The term photon storage is used in a general sense and the issue of the carrier or phase information lossis not addressed here. L. V. Butov, J. Phys. Condens. Matter , R1577 (2004). D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A.Burrus, Phys. Rev. B , 1043 (1985). M. Hagn, A. Zrenner, G. B¨ohm, and G. Weimann, Appl. Phys. Lett. , 232 (1995). A. Gartner, A. W. Holleitner, J. P. Kotthaus, and D. Schuh, Appl. Phys. Lett. , 052108 (2006). S. Zimmermann, A. O. Govorov, W. Hansen, J. P. Kotthaus, M. Bichler, and W. Wegscheider, Phys. Rev.B , 13414 (1997). A. T. Hammack, N. A. Gippius, Sen Yang, G. O. Andreev, L. V. Butov, M. Hanson, and A. C. Gossard,J. Appl. Phys. , 066104 (2006). T. Huber, A. Zrenner, W. Wegscheider, and M. Bichler, Phys. Stat. Sol. (a) , R5 (1998). Gang Chen, Ronen Rapaport, L. N. P ff eifer, K. West, P. M. Platzman, Steven Simon, Z. V¨or¨os, andD. Snoke, Phys. Rev. B , 045309 (2006). A. A. High, A. T. Hammack, L. V. Butov, L. Mouchliadis, A. L. Ivanov, M. Hanson, and A. C. Gossard,arXiv:0804.4886v1. A. A. High, A. T. Hammack, L. V. Butov, M. Hanson, and A. C. Gossard, Opt. Lett. , 2466 (2007). D. Yoshioka and A. H. MacDonald, J. Phys. Soc. Jpn. , 4211 (1990). X. Zhu, P. B. Littlewood, M. Hybertsen, and T. Rice, Phys. Rev. Lett. , 1633 (1995). Yu. E. Lozovik and O. L. Berman, JETP Lett. , 573 (1996). A. L. Ivanov, Europhys. Lett. , 586 (2002). C. Schindler and R. Zimmermann, arXiv:0802.3337. " ! $%&’()*)+, -./ -*/ FIG. 1: (a) GaAs / AlGaAs CQW band diagram. (b) Schematic of the photon storage circuit with animpedance-matched broadband transmission line. (a)
Laser (b)
GateVoltage ! storage (d)(c) DirectPL -200 -150 -100 -50 0 50 100 150Time [ns]Time [ns]IndirectPL Time [ns]-200 -150 -100 -50 0 50 100 150101001000 P L I n t en s i t y [ a . u .] P L I n t en s i t y [ a . u .] (e) Store Readout0 2 4 6 8 10 1210100 (f) ! ~ 250 ps FIG. 2: (a)–(d) Schematic of the photon storage and readout in the CQW device showing the sequence ofthe laser (a) and gate voltage (b) pulses as well as the emission of direct (c) and indirect (d) excitons. Theoperation principle of the device is described in the text. (e,f) Experimental implementation of the photonstorage in the CQW device. The gate voltage pulse V g = . τ readout ∼
250 ps. Thefall time and FWHM of the readout signal are both 2.5 ns.
90 795 800 805 810 020406080100120
790 795 800 805 810 020406080100120 P L P ea k W a v e l eng t h [ n m ] Laser offGate onGate off T i m e [ n s ] P L W a v e l eng t h [ n m ] I n t en s i t y [ a . u .] Laser offGate on (d) (c)(b)(a) T i m e [ n s ] P L W a v e l eng t h [ n m ] I n t en s i t y [ a . u .] Store Readout
Store
FIG. 3: Evolution of emission spectra during storage and readout for (a,b) the refined system employingan impedance-matched broadband transmission line and (c,d) the proof-of-principle system employing dc-suited wiring. The applied voltage is V g = . n + PL is seen at λ (cid:38)
805 nm during the laser pulse in (c). (b,d) Themean emission peak wavelength ¯ λ peak = (cid:82) λ I ( λ )d λ / (cid:82) I ( λ )d λ for the spectra presented in (a,c). The refinedsystem eliminates the emission oscillations su ff ered by the proof-of-principle system after the voltage pulse.ered by the proof-of-principle system after the voltage pulse.