Neuromorphic Computing:

Neuromorphic computing is an alternative computing architecture, which is developed in analogy with the biological brain 🧠. It is based on networks of artificial neurons. The connections between the neurons are carefully chosen such that it simulates the right relation between input and output data. Finding the right connection weights is known as the training of neural network. Commonly training is a time consuming and resource intensive process. However, training in reservoir computing, which is a form of neural network, is relatively easy. We recently proposed a exciton-polariton based reservoir computing device.

Moreover, we have generalized the reservoir computing platform for quantum information processing. It can perform various tasks involving quantum information with greater efficiency.

Exciton-polaritons:

In open quantum systems, constituent particles can enter into (gain) and leave from (decay) the system. Such systems are well described by quantum master equations. When the rate of gain exactly balances the rate of decay, a system reaches its steady state. For an imbalance between gain and decay, a system goes through non-steady dynamics. Both steady and non-steady properties of open systems are useful for many applications.

Exciton-polaritons formed in semiconductor microcavities are an open system, where external optical excitation can introduce new exciton-polaritons in the system, which can then spontaneously decay. Exciton-polaritons are considered useful for classical and quantum information processing. They are also important for studying fundamental physics. For example, typically Bose-Einstein condensation (BEC) is observed at ultracold temperature. Exciton-polaritons also form BEC, but at much higher temperature, e.g., at room temperature.

Anderson Localization

The motion of a particle in a disordered medium can be thought as a series of scattering events. Classically, the large scale motion turns out to be diffusive. A scattering event can be considered equivalent to a random phase kick to the wave function. Thus, the phase of the wave function would be totally scrambled when travelled distance is large compared to the mean free path. The phase of the wave function is thus expected to be unimportant for the large scale motion. Discarding the phase leads the motion to diffusive in nature.

Interference

In the classical picture, one neglects all possibilities of interference effect! A careful analysis shows that interference effects can be important. In fact, in certain conditions the interference effects can totally overrule the classical paradigm of diffusion and induce the so-called Anderson localization. Anderson localization is the localization of a single particle wave function in disordered media due to random scattering.

Anderson transition

Anderson localization has several implications, such as the Anderson metal-insulator transition. In a disordered system, particle can either be diffusive or be Anderson localized. When a charged particle is diffusive, it can conduct electrical current and thus behaves like a metal. However, when the particle is localized, it cannot transport electrical current and hence is an insulator. A transition from the metallic regime to the insulating regime is known as the Anderson metal-insulator transition or simply the Anderson transition. In order to achieve such transition, one would need to tune energy or the disorder strength. The point at which this transition takes place is called the mobility edge. The Anderson transition can be characterized by the localization length ( a length scale associated to localization). The localization length is infinite for a diffusive wave function and is finite and smaller than the system size for a localized particle. When a tuning parameter (x) approaches to the mobility edge (x_c) from the localized side, the localization length diverges: \xi~|x-x_c|^\nu, where $\nu$ is known as the critical exponent. This form of \xi is independent of the microscopic details of the system, and in fact '\nu=1.57' is constant for all systems forming a universality class. A universality class depends on the underlying symmetries of the Hamiltonian.

The physics of Anderson localization is not particular to the quantum particle but also applicable to the classical waves, light, microwaves, sound waves etc.

Coherent backscattering

Coherent backscattering (CBS) is an interference phenomenon occurring in disordered systems. When particles(waves) travel though disordered media, it has an extra probability density along the backward direction of its initial momentum. It can be realised in many different experimental set-ups. We are in particular interested in the configuration, where an initial plane wave launched with a momentum 'k_0'. After the propagation of time 't', which is larger than the transport mean free time, a peak appears in the backward direction of the momentum distribution. The centre of the peak is exactly -k_0. This peak is called the CBS peak. The existence of CBS peak does not imply Anderson localization, however, a well visible CBS-peak indicates the right direction towards the Anderson localization regime, it is a precursor of Anderson localization. The CBS effect is also known as the weak localization effect.

CBS can be explained by the maximally crossed diagram, where two Green's functions are connected though two maximally crossed infinite series of scattering lines. This diagram can be visualise by two counter propagating waves experience same series of scattering events, on average.

Coherent forward scattering

While coherent backscattering effect is known for decades now, the coherent forward scattering (CFS) is introduced only few years back in 2012 [here]. It is numerically discovered that, in presence of the Anderson localization, the momentum distribution has a second peak appears at exactly opposite to the CBS peak, i.e., the forward direction in the momentum distribution. In the bulk, existence of the CFS peak is conditional to the presence of the Anderson localization. This conditional existence makes CFS peak a reliable tool to analyse Anderson localization.

The diagrammatic explanation of the CFS peak is given by combinations of two maximally crossed diagrams. In simplistic picture, one can imagine CFS as the backscattering of the CBS peak. However, the probability amplitude for this process is much lower than the total CFS contribution. It is realised that the CFS constitutes much more complex higher order processes, which makes it non-perturbative. In a different approach, CFS dynamics can be associated with the local energy level correlations.