Office: G–10–11 Allen Hall, G–14–16 Lab, 104 OEH Lab
Phone: (412) 624–9007
Lab Phone: (412) 624–5870, (41
Graduate Students Former Students
David W. Snoke
Professor
Ph.D., 1990, University of Illinois at Urbana–Champaign
David W. Snoke is an undergraduate advisor.
Bose–Einstein Condensation of Excitons and Polaritons in Two and Three Dimensions
Bose–Einstein condensation is one of the most fascinating phase transitions in physics. When an ensemble of bosons is cooled to below a critical temperature, a macroscopic number of them will be attracted to occupy a single quantum state. This phenomenon, known as "spontaneous symmetry breaking," leads to super fluidity, superconductivity, and other fascinating effects.
Excitons, which are pair states of excited electrons and holes in a solid, are bosons and can undergo Bose–Einstein condensation under certain conditions. Since excitons are created by photons and can convert into photons, exciton motion essentially corresponds transport of optical energy. But because excitons have an effective mass, they move much more slowly than photons and therefore can undergo a spontaneous phase transition to a superfluid state just like atoms. One way of looking at an exciton condensate is that it corresponds to the spontaneous appearance of optical phase coherence even without lasing, i.e. "coherence without stimulated emission."
A polariton is a mixed state of an exciton and a photon. Since they are more photon–like than a simple exciton, the distinction between Bose–Einstein condensation of polaritons and lasing is less well defined; one can call spontaneous coherence in this system a "polariton laser." In principle, spontaneous coherence of polaritons can occur even at room temperature.
We create excitons or polaritons in semiconductor samples at liquid helium temperatures via an intense, ultrafast (picosecond or femtosecond) laser pulse and then examine the evolution of their momentum distribution and spatial distribution by detecting the light they emit, either via a time–gated CCD camera with 5 ns resolution, time–correlated photon counting with 40 ps resolution, a streak camera with 5 ps resolution, or pulse–probe methods with subpicosecond resolution. We also collaborate with theorists to answer fundamental questions about exciton and polariton condensates.
We collect the excitons and polaritons in traps in a semiconductor in two different ways. A trap can be made for excitons in GaAs or InGaAs quantum wells, when an inhomogeneous electric field is applied perpendicular to the plane of the wells. The excitons become polarized and move in response to a gradient in the electric field. We also can stretch the 2D sample slightly to create a hydrostatic expansion. Excitons are attracted to a region in the crystal which is expanded.
Several claims of Bose condensation of exitons have been made in the past ten years, but there is still debate. By taking images of the excitons and polaritons as they collect in a trap, we hope to provide definitive evidence of this novel effect.
Nonlinear Optics in Semiconductor Nanostructures
In electronics, the transistor plays an essential role as a switch by which one electrical signal turns another electrical signal on and off. Can we do the same thing with light beams? If we could make an "optical transistor" by which one light beam switches another one, we could make an optical computer in which all signals were carried by light instead of electrical signals. This would revolutionize technology in the way the electronic transistor did 50 years ago.
One way to do this is with nonlinear optics. In "linear" optics, the absorption and reflection coefficients of a medium are not dependent on the light intensity. In nonlinear optics, these coefficients can depend on the intensity, polarization, and wavelength of light. Therefore one can devise many schemes in which the presence of one light beam affects the transmission of another.
Besides optical–optical interactions, two other important effects are electro–optics and magneto–optics, in which an electric field or a magnetic field cause a shift of the optical properties of a material. These effects can be used for optical communications and memory devices.
In a "coupled quantum well" system, two very thin layers of semiconductor (about 6 nm, that is, 6 billionths of a meter) lie side by side. When electric field is applied to the sample, negative charges accumulate in one layer (or "well") and positive charges accumulate in the other one. There is a thin barrier in between the two layers, and quantum mechanics allows charge to "tunnel" from one layer to the other without hopping over the barrier; as if passing magically through a wall.
The optical properties of this system depend sensitively on all kinds of things. We see large shifts of the luminescence wavelength with laser intensity, with electric field, and with magnetic field, in addition to shifts due to stress and temperature. We can control these shifts and use them to modulate the light signals.
Excitonic Circuits
In a quantum well, when an electric field is applied perpendicular to the plane of the wells, the excitons become polarized and move in response to a gradient in the electric field. With the use of electron beam lithography, we can make complicated gate structures on the surface of a quantum well wafer to control the movement of excitons. Our goal is to test the viability of these excitonic circuits for light harvesting and other electro–optical applications.
Bose–Einstein condensation is one of the most fascinating phase transitions in physics. When an ensemble of bosons is cooled to below a critical temperature, a macroscopic number of them will be attracted to occupy a single quantum state. This phenomenon, known as "spontaneous symmetry breaking," leads to super fluidity, superconductivity, and other fascinating effects.
Excitons, which are pair states of excited electrons and holes in a solid, are bosons and can undergo Bose–Einstein condensation under certain conditions. Since excitons are created by photons and can convert into photons, exciton motion essentially corresponds transport of optical energy. But because excitons have an effective mass, they move much more slowly than photons and therefore can undergo a spontaneous phase transition to a superfluid state just like atoms. One way of looking at an exciton condensate is that it corresponds to the spontaneous appearance of optical phase coherence even without lasing, i.e. "coherence without stimulated emission."
A polariton is a mixed state of an exciton and a photon. Since they are more photon–like than a simple exciton, the distinction between Bose–Einstein condensation of polaritons and lasing is less well defined; one can call spontaneous coherence in this system a "polariton laser." In principle, spontaneous coherence of polaritons can occur even at room temperature.
We create excitons or polaritons in semiconductor samples at liquid helium temperatures via an intense, ultrafast (picosecond or femtosecond) laser pulse and then examine the evolution of their momentum distribution and spatial distribution by detecting the light they emit, either via a time–gated CCD camera with 5 ns resolution, time–correlated photon counting with 40 ps resolution, a streak camera with 5 ps resolution, or pulse–probe methods with subpicosecond resolution. We also collaborate with theorists to answer fundamental questions about exciton and polariton condensates.
We collect the excitons and polaritons in traps in a semiconductor in two different ways. A trap can be made for excitons in GaAs or InGaAs quantum wells, when an inhomogeneous electric field is applied perpendicular to the plane of the wells. The excitons become polarized and move in response to a gradient in the electric field. We also can stretch the 2D sample slightly to create a hydrostatic expansion. Excitons are attracted to a region in the crystal which is expanded.
Several claims of Bose condensation of exitons have been made in the past ten years, but there is still debate. By taking images of the excitons and polaritons as they collect in a trap, we hope to provide definitive evidence of this novel effect.
Nonlinear Optics in Semiconductor Nanostructures
In electronics, the transistor plays an essential role as a switch by which one electrical signal turns another electrical signal on and off. Can we do the same thing with light beams? If we could make an "optical transistor" by which one light beam switches another one, we could make an optical computer in which all signals were carried by light instead of electrical signals. This would revolutionize technology in the way the electronic transistor did 50 years ago.
One way to do this is with nonlinear optics. In "linear" optics, the absorption and reflection coefficients of a medium are not dependent on the light intensity. In nonlinear optics, these coefficients can depend on the intensity, polarization, and wavelength of light. Therefore one can devise many schemes in which the presence of one light beam affects the transmission of another.
Besides optical–optical interactions, two other important effects are electro–optics and magneto–optics, in which an electric field or a magnetic field cause a shift of the optical properties of a material. These effects can be used for optical communications and memory devices.
In a "coupled quantum well" system, two very thin layers of semiconductor (about 6 nm, that is, 6 billionths of a meter) lie side by side. When electric field is applied to the sample, negative charges accumulate in one layer (or "well") and positive charges accumulate in the other one. There is a thin barrier in between the two layers, and quantum mechanics allows charge to "tunnel" from one layer to the other without hopping over the barrier; as if passing magically through a wall.
The optical properties of this system depend sensitively on all kinds of things. We see large shifts of the luminescence wavelength with laser intensity, with electric field, and with magnetic field, in addition to shifts due to stress and temperature. We can control these shifts and use them to modulate the light signals.
Excitonic Circuits
In a quantum well, when an electric field is applied perpendicular to the plane of the wells, the excitons become polarized and move in response to a gradient in the electric field. With the use of electron beam lithography, we can make complicated gate structures on the surface of a quantum well wafer to control the movement of excitons. Our goal is to test the viability of these excitonic circuits for light harvesting and other electro–optical applications.
Selected Publications
- "Actively Tuned and Spatially Trapped Polaritons," R. Balili, D.W. Snoke, L. Pfeiffer, and K. West, Applied Physics Letters 88, 031110 (2006)
- "Bose-Einstein Condensation of Microcavity Polaritons in a Trap," R. Balili, V. Hartwell, D.W. Snoke, L. Pfeiffer and K. West, Science 316, 1007 (2007)
- "Long-range Transport in Excitonic Dark States in Coupled Quantum Wells," D. Snoke, S. Denev, Y. Liu, L. Pfeiffer, and K. West, Nature 418, 754 (2002).
- "Polariton Lasing vs. Photon Lasing in a Semiconductor Microcavity," H. Deng, G. Weihs, D. Snoke, J. Bloch, and Y. Yamamoto, Proc. National Acad. of Sciences 100, 15318 (2003).
- "Mechanism of Luminescence Ring Pattern Formation in Quantum Well Structures: Optically-Induced In-Plane Charge Separation," R. Rapaport, Gang Chen, D. Snoke, S.H. Simon, L. Pfeiffer, K. West, Y. Liu, and S. Denev, Physical Review Letters 92, 117405 (2004).
- "Lateral Diffusion of Excitons in Double Quantum Well Structures," Z. Vörös, R. Balili, D.W. Snoke, L. Pfeiffer, and K. West, Physical Review Letters 94, 226401 (2005).
- "Trapping Excitons in a Two-Dimensional In-Plane Harmonic Potential: Experimental Evidence for Equilibration of Indirect Excitons," Z. Vörös, D.W. Snoke, L. Pfeiffer, and K. West, Physical Review Letters 97, 016803 (2006).
