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.
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.
Quantum memories for light lie at the heart of long-distance provably-secure communication [1], while containing the potential to help break current encryption methods [2], and allow better measurement of quantities than ever before [3]. Demand for a functioning quantum memory is therefore at a premium. Unfortunately, the same properties of light that make it such an effective carrier of quantum information make it difficult to store. Furthermore, by the laws of quantum mechanics, storage must be achieved without measurement to preserve the quantum state. A quantum memory needs to have an efficiency approaching unity without adding noise to the state, and storage times from milliseconds to seconds. Ideally it would also have a high bandwidth and be able to store many pieces of information simultaneously. Many different techniques are currently being developed and much experimental progress has been made over the past few years, with: efficiencies approaching 90% [4]; storage times of over seconds [5]; bandwidths of gigahertz [6, 7]; and over 1000 pieces of information stored at one time [8]. These results were, however, achieved using different memory schemes in different storage media. The challenge now is to reproduce these results with one memory. This thesis focuses on extending the gradient echo memory (GEM) scheme, which shows great promise due to the high efficiencies achieved (87%) [4]. GEM has also been used to demonstrate temporal compression and stretching of pulses, as well as a capacity to arbitrarily resequence stored information [9] and the interference of initially time-separated pulses [10]. Firstly, we demonstrate the noiseless nature of GEM storage in a warm vapour cell to prove that the output from the memory is the best-possible copy of the input allowed by quantum mechanics. We show GEM’s ability to coherently and precisely spectrallymanipulate stored information by having fine control over the memory’s frequency gradient, with potential applications for dynamic conditioning of information inside quantum networks [11]. We demonstrate cross-phase modulation of a stored light pulse with an additional optical field, a process with applications in quantum computing [12]. We also carry out storage of different spatial modes and arbitrary images, demonstrating the potential for orders of magnitude improvement in storage capacity. We then switch from warm vapour cells to cold atomic ensembles to improve the storage time of GEM, seeing a maximum coherence time of 350 μs (seven times that of the warm vapour system) and achieving efficiencies of up to 80%, on a par with the highest efficiency achieved with a cold atomic ensemble [13]. In the process we developed an ultra-dense cold atomic cloud with potential applications in a range of quantum optics experiments. Cold atoms, and the small volumes they occupy, also allowed us to develop an alternative to using magnetic field gradients for our alkali-atom memories in the form of a light-field gradient. This holds promise for extremely fast gradient switching and fine control over the gradient. We also present a digital locking code with application in a range of quantum optics experiments.
We investigate the properties of a recently proposed gradient echo memory (GEM) scheme for information mapping between optical and atomic systems. We show that GEM can be described by the dynamic formation of polaritons in k space. This picture highlights the flexibility and robustness with regards to the external control of the storage process. Our results also show that, as GEM is a frequency-encoding memory, it can accurately preserve the shape of signals that have large time-bandwidth products, even at moderate optical depths. At higher optical depths, we show that GEM is a high fidelity multimode quantum memory.
Gradient echo memory (GEM) stores and retrieves photon wave packet in forward direction with high efficiency and fidelity using photon-echo mechanism. It is an important technique for quantum memory applications. By breaking the continuity of the gradient absorption structure, the scheme becomes gradient frequency comb (GFC), which is a hybrid of GEM and atomic frequency comb (AFC). To elucidate the non-trivial field-atom evolution of gradient echo, we derive its exact analytical solution in a medium of arbitrary optical thickness subjecting to any linear gradient of transition frequency, and discuss its physical processes. Based on this solution, we further suggest and analysis two types of GFC, one with stepwise gradient and the other with discontinuous gradient.
Quantum memories are an integral component of quantum repeaters—devices that will allow the extension of quantum key distribution to communication ranges beyond that permissible by passive transmission. A quantum memory for this application needs to be highly efficient and have coherence times approaching a millisecond. Here we report on work towards this goal, with the development of a 87 Rb magneto-optical trap with a peak optical depth of 1000 for the D2 F = 2 → F ' = 3 transition using spatial and temporal dark spots. With this purpose-built cold atomic ensemble we implemented the gradient echo memory (GEM) scheme on the D1 line. Our data shows a memory efficiency of 80 ± 2% and coherence times up to 195 μ s, which is a factor of four greater than previous GEM experiments implemented in warm vapour cells.
This thesis demonstrates an efficient quantum memory that for the first time preserves more quantum information than it loses. Beyond this, it describes how even higher efficiency may be realised without sacrificing the other performance characteristics that are required for a practical device. A quantum memory is a device to store and recall the quantum state of light. Such a memory will be required for most applications of the emerging field of quantum information. The closest practical application is quantum repeaters for long distance encryption. A more distant target is quantum computing. Yet demonstrations of quantum memory to date fall far short of the performance required for repeaters, and further short of that for quantum computing. For these applications, high performance will be required in terms of 3 parameters: long storage time, high efficiency, and a large mode-capacity. Prior to this work, the storage time was the only paramter to have been demonstrated near the required level[1], and that only in a classical regime. The primary result of this thesis is to demonst rate a memory with an efficiency close the required level (70% is measured), and confirm its quantum nature with noise measurements. This represents the first quantum memory with efficiency greater than 50% and the first to operate unconditionally above the "no-cloning limit". The demonstration used the same storage medium as for the previous long-term storage experiment (Pr{u00B3}{u207A}:Y{u2082}Si0{u2085} (PrYSO)), and could in principle reach the same long storage times. The technique used is an optical "gradient echo", an optical equivalent to the long studied gradient echo technique used in Nuclear Magnetic Resonance (NMR). Aside from it's practicality for demonstrations, a gradient-echo also offers a powerful handle for manipulating stored light. However it is more complex than related memory techniques because it employs a spatially-varying medium. This becomes crucial when the optical depth (and memory efficiency) is increased; propagation effects mean the light is stored very differently than in other techniques. A simple linear-response model is used to gain insight into this high optical depth regime. As a result, some new properties are identified which may increase the efficiency in practical circumstances and improve flexibility. Of particular note, it's found that the space-dependence can be used to hide one narrow transition with another. This allows the somewhat unintuitive notion that a light pulse can fully traverse a medium without exciting a transition that it is resonant with. The spectral-hiding property has promise to overcome the problem with simultaneously acheiving all three parameters required for quantum memories. The problem is related to the preparation of available rare-earth ion doped materials. To acheive high efficiency and storage times, these require spectral holeburning whose bandwidth is limited by the splittings of spin levels. Methods exist to create high bandwidth delays lines with holeburning[2], but they cannot be efficient or long-lived. By utilising the spectral-hiding property of the gradient echo, methods to overcome this limitation are described for the first time.
Photon echo schemes are excellent candidates for high efficiency coherent optical memory. They are capable of high-bandwidth multipulse storage, pulse resequencing and have been shown theoretically to be compatible with quantum information applications. One particular photon echo scheme is the gradient echo memory (GEM). In this system, an atomic frequency gradient is induced in the direction of light propagation leading to a Fourier decomposition of the optical spectrum along the length of the storage medium. This Fourier encoding allows precision spectral manipulation of the stored light. In this Letter, we show frequency shifting, spectral compression, spectral splitting, and fine dispersion control of optical pulses using GEM.