Abstract
The gradient echo memory (GEM) technique is a promising candidate for real devices due to its demonstrated performance, but to date high performance experiments can only be described numerically. In this paper we derive a model for GEM as a cascade of infinite interconnected harmonic oscillators. We take a quantum input–output approach to analyse this system, describing the read and write processes of GEM each as a linear-time-invariant process. We provide an analytical solution to the problem in terms of transfer functions which describe the memory behaviour for arbitrary inputs and operating regimes. This allows us to go beyond previous works and analyse the storage quality in the regimes of high optical depth and memory-bandwidth comparable to input bandwidth, exactly the regime of high-efficiency experiments.
Highlights
Of quantum memory is a highly active field
In this paper we present a fully quantum mechanical description of the gradient echo memory (GEM) based on a quantum input–output model [32]
This is a familiar scenario in many areas of engineering such as control theory and signal processing, where the common approach is to use the concept of linear time-invariant (LTI) systems [38]
Summary
We may think of a GEM as a section of a material through which light is passed as shown in figure 1 (bottom). These are shown to be the quantum operator equations that lead to the Maxwell–Bloch equations in [28] and our full quantum model represents faithfully the dynamics of GEM in the weak atomic excitation regime. Derivation of the model We consider a series of cavities connected as a cascade network as shown in figure 1. In our model we have a set of elements connected in series, which corresponds to a cascade quantum system as studied in quantum optics [32, 33, 37] In this case, each cavity is represented by the parameters. Since there is a one-to-one correspondence between the position z and the detuning ξ , throughout the paper we will refer to ξ as detuning or spatial variable
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