Negative Mass States Research Articles

Unstable and stable regimes of polariton condensation

Modulational instabilities play a key role in a wide range of nonlinear optical phenomena, leading e.g. to the formation of spatial and temporal solitons, rogue waves and chaotic dynamics. Here we experimentally demonstrate the existence of a modulational instability in condensates of cavity polaritons, arising from the strong coupling of cavity photons with quantum well excitons. For this purpose we investigate the spatiotemporal coherence properties of polariton condensates in GaAs-based microcavities under continuous-wave pumping. The chaotic behavior of the instability results in a strongly reduced spatial and temporal coherence and a significantly inhomogeneous density. Additionally we show how the instability can be tamed by introducing a periodic potential so that condensation occurs into negative mass states, leading to largely improved coherence and homogeneity. These results pave the way to the exploration of long-range order in dissipative quantum fluids of light within a controlled platform.

Position and momentum uncertainties of a particle in a V-shaped potential under the minimal length uncertainty relation

We calculate the uncertainties in the position and momentum of a particle in the 1D potential [Formula: see text], [Formula: see text], when the position and momentum operators obey the deformed commutation relation [Formula: see text], [Formula: see text]. As in the harmonic oscillator case, which was investigated in a previous publication, the Hamiltonian [Formula: see text] admits discrete positive energy eigenstates for both positive and negative mass. The uncertainties for the positive mass states behave as [Formula: see text] as in the [Formula: see text] limit. For the negative mass states, however, in contrast to the harmonic oscillator case where we had [Formula: see text], both [Formula: see text] and [Formula: see text] diverge. We argue that the existence of the negative mass states and the divergence of their uncertainties can be understood by taking the classical limit of the theory. Comparison of our results is made with previous work by Benczik.

Negative-mass transport in semiconductor diodes

An analysis of high-field electron transport in a semiconductor diode is presented using a simple kinetic model. A cosine band structure is assumed for the conduction band and the diode is taken to be short enough for the rate of energy-relaxation collisions to be negligible. The drift velocity of the electrons is determined by momentum-relaxation collisions independent of the applied electric field and the band structure, and transfer or tunneling to other valleys or bands is ignored. The analysis is applied to GaN, and conditions for the appearance of a negative differential resistance (NDR) associated with the negative-mass states in the band are derived for the regime of diode lengths and fields in which Bloch oscillations do not occur. It is shown that NDR in this regime occurs over a limited range of diode lengths and fields. Lengths and fields corresponding to breakdown conditions are explicitly avoided.

The Relativistic One-Dimensional Square Potential

The one-dimensional Dirac equation is applied to the cases of a particle bound in a square well and of a beam of particles impinging upon a square potential. The solutions are compared to the Schrödinger solutions, and the effect of the negative mass states is discussed.

Theory of Cyclotron Resonance Absorption by Negative-Mass Holes in Germanium

The effect of orbital quantization on cyclotron resonance absorption by negative-mass heavy holes in germanium is considered. The Landau level system for the heavy holes in the approximation of an axial energy surface is computed with an equation derived by Firsov. A semiclassical technique is used to compute the cyclotron absorption by the holes in negative mass states under thermal equilibrium conditions. It is shown that at low temperatures the absorption is markedly less than that which would be calculated by the usual classical transport theory; at 4.2\ifmmode^\circ\else\textdegree\fi{}K and 30 kMc/sec the absorption resonance essentially disappears. Similar effects are present, in principle, for any nonellipsoidal energy surface. The bearing of these calculations on several recent experiments is discussed.

Some results on analytic functions in local field theory

Lorentz invariance, local commutativity, and the absence of negative mass states imply that the vacuum expectation value and the Fourier transform of the retarded commulator of a product of field operators are boundary values of analytic functions. The cases of four and five local scalar fields are investigated in the spirit of the approach of Källén and Wightman. It is shown that the domain of analyticity of the vacuum expectation value in x-space contains that of there retarted commutator in p-space. A computation of the real points of these domains is discussed in an appendix.