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# Coherent ultrafast dynamics

Coherence in light–matter interaction is a necessary ingredient if light is used to control the quantum state of a material system. Quantum coherence and coherent dynamics in well-characterized, selected quantum systems, primarily III-V SK-quantum dots, is being analyzed and controlled.

## Quantum coherence at room-temperature

- FROSCH measurement of pulse shape modification through coherent light-matter interaction.
- © Kolarczik et al.,Nat. Commun.4,2953(2013)

The signature of Rabi oscillations is retained at room temperature and under conditions of electrical pumping, adding the QD inversion as an additional control parameter. Adjusting the QD population via the electrical current allows for switching the modulations of the pulse shape, thus controlling coherent effects through population. These effects have the potential to be exploited for ultrafast modulation of optical signals. For telecommunications applications it is advised to keep the light intensity at levels low enough to avoid a distortion of the bit sequence due to unwanted coherent modulation.

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## Pump-probe quantum-state tomography

- (left) 3D views of the Wigner functions. Comparing an amplified coherent state with an amplified vacuum state and the vacuum state as a reference. (right) Pump-Probe QST. Observing the transformation in the Wigner function of the probe state before, durin
- © Grosse et al.,OE22,32520(2014)

In the lab we have combined the technique of quantum state tomography with a two-colour pump-probe setup. This allows us to see, in an ultrafast time window, how the quantum state of an optical transition is transformed when neighbouring energy levels are pumped in a gain medium. We can find out how the population inversion is affected by scattering of carriers with other energy levels and relate this to the gain and noise performance of the device.

THE QUANTUM STATE

There are many representations of the quantum state of a system, with the density matrix and the Wigner function being just a couple. For a single mode of the optical field, the Wigner representation is very intuitive. Thinking of a monochromatic light as an electromagnetic wave that has a given amplitude and phase, it would be represented by one point in quadrature diagram, where the axes are termed the amplitude and phase quadratures. The quadratures are actually the amplitudes of a decomposition of the wave in a sine/cosine basis. Because of the Heisenberg uncertainty principle applying to these noncommuting variables, the position of the dot is statistically smeared out. There is a probability distribution describing the quantum state. This is the Wigner function. Intriguingly, even if there are no photons in the mode and the mean field is zero (the vacuum state), there are still fluctuations in quadrature amplitudes.

TOMOGRAPHY

The Wigner function can be measured in the continuous variable regime, using a bright reference laser as a local-oscillator, and interfering it on a symmetric beamsplitter with the optical mode of interest. Careful balancing of the detected photocurrents suppresses all intensity fluctuations from the local-oscillator, thus allowing the very tiny quantum fluctuations of the signal beam to be observed (which are effectively amplified by the local-oscillator mean field). Histograms of the fluctuations are acquired for many phase angles. These are then tomographically processed via an inverse Radon transformation to arrive at the Wigner function.

APPLYING PUMP-PROBE QST TO OPTICAL AMPLIFIERS

In the Figure opposite, one can see that the gain medium, a semiconductor optical amplifier (SOA) based on quantum dots, produces a very noisy state (large circle). This is due to both amplified spontaneous emission, and amplified noise from the input state (even if it is in a vacuum state). Less than a picosecond after the pump and probe have overlapped in the SOA waveguide, not only the gain of the device is momentarily depleted, but also the noise. Analyzing the noise (the width of the circle), one can determine that the population inversion itself was depleted by the presence of the pump light which depleted a higher energy level of carriers, hence demonstrating the coupling/scattering between internal energy levels of the quantum dots.

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## Publications

**2016**

Lingnau, B., Lüdge, K., Herzog, B.,Kolarczik, M., Kaptan, Y., Woggon, U. and Owschimikow, N., Physical Review B **94**, 014305 (2016). *Ultrafast gain recovery and large nonlinear optical response in submonolayer quantum dots. *DOI: 10.1103/PhysRevB.94.014305

**2015**

Herzog, B., Owschimikow, N.,Schulze, J.-H., Rosales, R., Kaptan, Y., Kolarczik, M., Switaiski, T., Strittmatter, A., Bimberg, D., Pohl, U.W. and Woggon U., Applied Physics Letters **107**, 201102 (2015). *Fast gain and phase recovery of semiconductor optical amplifiers based on submonolayer quantum dots. *DOI: 10.1063/1.4935792

Kolarczik, M., Owschimikow, N., Herzog, B., Buchholz, F., Kaptan, Y.I. and Woggon, U., Physical Review B **91**, 235310 (2015). *Exciton dynamics probe the energy structure of a quantum dot-in-a-well system: The role of Coulomb attraction and dimensionality. *DOI: 10.1103/PhysRevB.91.235310

**2014**

Grosse, N.B., Owschimikow, N., Aust, R., Lingnau, B., Koltchanov, A., Kolarczik, M., Lüdge, K. and Woggon, U., Optics Express **22**, 32520 (2014). *Pump-probe quantum state tomography in a semiconductor optical ampliﬁer. *DOI:10.1364/OE.22.032520

Owschimikow, N., Kolarczik, K., Kaptan, Y.I., Grosse, N.B. and Woggon, U., APL **105**, 101108 (2014). *Crossed excitons in a semiconductor nanostructure of mixed dimensionality. *DOI: 10.1063/1.4895558

Kaptan, Y. and Röhm, A. and Herzog, B. and Lingnau, B. and Schmeckebier, H. and Arsenijevic, D. and Mikhelashvili, V. and Schöps, O. and Kolarczik, M. and Eisenstein, G. and Bimberg, D. and Woggon, U. and Owschimikow, N. and Lüdge, K., Applied Physics Letters **119**, 191105 (2014). *Stability of quantum-dot excited-state laser emission under simultaneous ground-state perturbation. *DOI: 10.1063/1.4901051

Kaptan, Y. and Schmeckebier, H. and Herzog, B. and Arsenijevic, D. and Kolarczik, M. and Mikhelashvili, V. and Owschimikow, N. and Eisenstein, G. and Bimberg, D. and Woggon, U., Applied Physics Letters **104**, 261108 (2014). *Gain dynamics of quantum dot devices for dual-state operation. *DOI: 10.1063/1.4885383

**2013**

Kolarczik, M., Owschimikow, N., Korn, J., Lingnau, B., Kaptan, Y., Bimberg, D., Schöll, E., Lüdge, K. and Woggon, U., Nature Communications **4**, 2953 (2013). *Quantum coherence induces pulse shape modiﬁcation in a semiconductor optical ampliﬁer at room temperature.* DOI: 10.1038/ncomms3953

Switaiski, T., Woggon, U., Angeles, D.E.A., Hoffmann, A., Schulze, J.-H., Germann, T.D., Strittmatter, A. and Pohl, U.W., Physical Review B **88**, 035314 (2013). *Carrier dynamics in InAs / GaAs submonolayer stacks coupled to Stranski-Krastanov quantum dots.* DOI: 10.1103/PhysRevB.88.035314