Frozen light could give quantum computers memory

Brian Julsgaard, Jacob Friis Sherson, J. I. Cirac +2 more

Manjin Zhong

This thesis investigates the coherence properties of the hyperfine transitions of the 151Eu3+ ions in Eu3+:Y2SiO5 and evaluates the potential of developing quantum memories using these transitions. Quantum memories for light with long storage times are required for quantum commu- nication applications. For these memories to be useful they need to have storage times long compared to the transmission times across the communication network. For a global optical communication network this requires storage time longer than 100 ms. Rare-earth doped crystals have been identified as a suitable storage material. The storage time of these systems is limited by the coherence time of the hyperfine transitions of the optically active rare-earth ions. In previous work it had been demonstrated that coherence times as long as 1.4 seconds could be achieved for hyperfine transitions in Pr3+:Y2SiO5 by ap- plying a particular magnetic field such that the first order Zeeman shift of the transition nulled. This technique is known as zero first-order Zeeman (ZEFOZ). Due to the relatively large second order Zeeman efficient of the transitions in Pr3+:Y2SiO5, an extension of the coherence time, significantly beyond the 1.4 second mark using ZEFOZ, is not expected. However, it has been predicted that coherence times more than two orders of magnitude longer could be achieved in Eu3+:Y2SiO5 due to the smaller second order Zeeman shifts associated with the relevant hyperfine transitions. The dominant decoherence mechanism for the hyperfine transitions in diluted Eu3+:Y2SiO5 is the magnetic field perturbations caused by the random spin reconfigu- ration of the Y3+ ions in the host. By applying the ZEFOZ technique, previously used in Pr3+:Y2SiO5, the sensitivity of the transition’s frequency to environmental magnetic field perturbations was significantly reduced. Further, this strong ZEFOZ magnetic field was also shown to induce a frozen core around the Eu3+ ion, which resulted in a signifi- cant suppression of the reconfiguration of the nearby Y3+ spins. The combined effect of the reduced sensitivity and frozen core effect allowed a decoherence rate of 8 × 10−5 s−1 over 100 milliseconds to be demonstrated. The observed decoherence rate is at least an order of magnitude lower than that of any other system suitable for an optical quantum memory. Furthermore, by employing dynamic decoherence control, a coherence time of 370 ± 60 minutes was achieved. This 6 hour coherence time observed here opens up the possibility of distributing quantum entanglement via the physical transport of memories as an alternative to optical communications. It was found that even at the critical point alignment the observed coherence times showed that the Y3+ spin flips remain the dominant decoherence mechanism. To aid in the development of future strategies to further extend the coherence time beyond 6 hours, a study of the Y3+ spin dynamics in the frozen core was conducted. Four of the Y3+ sites were resolved and a complete mapping of all frozen-core Y3+ sites was limited by the inhomogeneity of the applied magnetic field. The Rabi frequency, the coherence time and lifetime as well as the interaction strength with the Eu3+ ion of one of these Y3+ ions were measured. The observed lifetime of the Y3+ ion is 27 s, which is four orders of magnitude longer than the low field value. With the technique developed, a detailed understanding of the frozen-core dynamics is possible, which would allow an extension of the hyperfine coherence time of the Eu3+ ion towards the lifetime limit. In summary, this thesis provides a detailed characterisation of the decoherence mecha- nisms of the hyperfine transitions in Eu3+:Y2SiO5. The potential of using rare-earth doped crystals for the long-term storage of quantum information with applications to long-range quantum communications is identified. The demonstrated long coherence time of the quantum transitions for information storage allows a new way of entanglement distribu- tion: entanglement is transported by physically transporting the memory crystal rather than the light. This approach opens a new regime for both quantum communication and fundamental tests of quantum mechanics.

Collin M. Trail, Barry C. Sanders

We model frozen light stored as a spin wave via electromagnetically induced transparency quantum-memory techniques in a Bose-Einstein condensate. The joint evolution of the condensate and the frozen light is typically modeled using coupled Gross-Pitaevskii equations for the two atomic fields, but these equations are only valid in the mean-field limit. Even when the mean-field limit holds for the host condensate, coupling between the host and the spin wave component could lead to a breakdown of the mean-field approximation if the host fluctuations are large compared the mean-field value of the spin wave. We develop a theoretical framework for modeling the corrections to the mean-field theory of a two-component condensate. Our analysis commences with a full second-quantized Hamiltonian for a two-component condensate. The field operators are broken up into a mean-field and a quantum fluctuation component. The quantum fluctuations are truncated to lowest non-vanishing order. We find the transformation diagonalizing the second-quantized approximate Hamiltonian and show that it can be described using the solutions to a system of coupled differential equations.

Morgan P. Hedges, Jevon J. Longdell, Yongmin Li +1 more

Sergey V. Gaponenko

In nanostructures where confinement of a light wave is manifested, the conditions of strong light–matter interaction become feasible. In this case, the approach based on the environment-sensitive probability of quantum transitions is no longer applicable. Instead, joint states of light and matter should be considered and their time evolution explored. The content of the previous Chapters 13 and 14 can then be treated as a perturbative description of light–matter interactions with a limited range of applicability. In this chapter a few representative examples are given where joint light–matter states bring an unprecedented flavor of nanophotonic engineering to frozen excited states for quantum memory devices and single photon sources for quantum computing. Cavity quantum electrodynamics in the strong coupling regime The regime of strong coupling of a quantum system with an electromagnetic field can be performed in a cavity with very high Q-factor, where light can survive for a reasonable time until it either leaves the cavity or dies through being absorbed by cavity imperfections. In a simplified picture, a photon once emitted stays within the cavity so long that it is absorbed again by the emitter (an imaginary two-level system, an atom or a quantum dot). Thus spontaneous emission appears to become reversible. In a more accurate presentation, an “atom+field” state develops which evolves via oscillations between the state | E , 0〉 (“excited atom, depleted cavity”) to the state | G , 1〉 (“de-excited atom, a photon in the cavity”).

Johanna L. Miller