First demonstration of optically controlled entanglement of the spin state of two quantum dots. Initialization, single-qubit, and two-qubit gates were demonstrated (submitted to Nature Physics).
Single-photon Bragg scattering and Time-Lenses for hybrid quantum memories
During this program period, we focused on three primary areas:
- Quantum theory of time lenses
Previous work on classical time lenses use a dispersive devices (e.g., grating or dispersive optical fiber) in combination with a phase modulator. Our goal has been to develop a full quantum theory for these devices to be able to make predictions for the behavior of a time lens. The quantum behavior of a dispersive optical fiber is well established, but there are complexities associated with the proper treatment of a phase modulator. We have worked to extend the recent work of Kumar and Prabhakar [IEEE J. Quantum. Electron. 45, 149 (2009)]. We recently found that Capmany and Fernandez-Pousa largely has solved this problem [J. Opt. Soc. Am. B 27, A119 (2010)]. We will not focus our efforts on using the Capmany-Fernandez-Pousa results to develop the time-lens theory. We anticipate that this analysis will be completed in Fall 2010 and submitted for publication.
- GAWBS noise in a highly nonlinear fiber
Another approach for frequency shifting light to make a hybrid memory is to use nonlinear Bragg scattering. In this process, a two-frequency laser beam pumps a material displaying a nonlinear refractive index, such as a highly nonlinear optical fiber. It is known that a process known as guides wave Brillouin scattering (GAWBS) causes excess noise in the spectral vicinity of the pump frequencies. To our knowledge, there has not been a study of GAWBS in the highly nonlinear fiber that we hope to use in the frequency-shifting process. We have found that the GAWBS noise is much stronger than anticipated, but is localized to within a few GHz of the pump frequency. This excess noise limits the Bragg scattering effect for frequency shifts larger than several GHz. Therefore, it may not be useful for connecting memories formed by two quantum dots that only have slightly different frequencies. On the other hand, resonance frequency differences less than a few GHz can be compensated using other methods (such as by using an off-resonance laser beam that causes an AC-Stark effect. This work will be discussed at the 2010 FiO/LS annual meeting and an abstract has been submitted to Photonics West 2011.
- Fiber tapering apparatus
To obtain large frequency shifts via Bragg scattering requires that the dispersive properties of the optical fiber can be tailored. We are developing a “flame brush” fiber tapering apparatus so that we can control the diameter of optical fibers and thus adjust their phase matching properties. In the coming year, we will demonstrate that we can achieve Bragg scattering in a tapered optical fiber whose diameter is chose to enhance the nonlinear optical interaction strength as well as the phase matching wavelengths.
The Maryland group has previously demonstrated the interference and detection of photons emitted from a pair of ions, thereby heralding the entanglement of the atomic quantum bits. However, the imaging system used to capture, detect, and analyze the heralding photons is not optimal, leaving room for future improvement; specifically, reductions in wavefront error would allow for more efficient fiber coupling. We have been working toward this end by attempting to measure and reduce aberrations induced by the glass window through which the photons from the ions must propagate. Initially, a wavefront sensor was used to quantify the wavefront error difference with and without the vacuum window in the imaging system (Figure 1). In agreement with our calculations, spherical aberration was significantly affected when the vacuum window was inserted into the imaging setup. In an attempt to reduce wavefront error, we have demonstrated a proof-of-concept reduction of spherical aberration using adaptive optics (Figure 2). However, practically useful improvements for fiber coupling are limited by the (poor) surface quality of our current deformable mirror. Specifically, it was discovered during experimentation that our Imagine Optics deformable mirror had lost flexibility and gained long-term deformations, likely due to improper curing of the epoxy. Collaboration with manufacturers Imagine Optics and Alpao have led to tests, currently underway, into probable errors in the manufacturing process used to create these mirrors. We expect to have mirrors delivered in the next several weeks.
Most recently, advanced ray tracing software has been implemented to recreate and improve the ion imaging setup. The predicted maximum theoretical efficiency (from ion to single-mode fiber) is around 76%; however, the maximum coupling seen in practice was around 30%. Through simulations using ZEMAX-EE, we are working to identify the causes of efficiency losses and to improve the setup for maximum photon coupling. In addition, we have investigated—with promising results—the reduction of spherical aberration with the addition of a single element. We believe the fiber-coupling efficiencies of the imaging system can be increased in practice to over 75%. These results, supported by physical measurements of aberrations, the potential for improved adaptive optics, and ray-tracing computer simulation and optimization, should in turn improve future ionic remote-entanglement experiments as well as coupled ion-photon (and quantum dot-photon) systems in general.
The Maryland Ion Trap group has investigated the use of hybrid quantum information within atomic and photonic systems for large-scale quantum networks as well as applications in quantum communication. At the same time, we are investigating next-generation technology that will enhance the atom-photon interface efficiency.
Coulomb (local) plus photonic (remote) quantum networks. Trapped ion qubits are conventionally entangled based on their local Coulomb interaction. However, this mechanism alone has limitations in scaling to very large numbers of qubits, or qubits separated by a long distance. Probabilistic photonic gates can fill this need, and such a connection suggests a new type of qubit architecture that exploits both types of quantum circuitry. Following the recent experiments from our group concerning two separated trapped ion qubits, we have modified the traps so that they can hold 2 ions, and we are currently implementing both types of gates (phonon and photon) on the ions.
We have trapped a single ion between two Fabry-Perot cavity mirrors, in order to enhance the light collection efficiency of single photons. We have successfully excited the atom from the side and collected fluorescence through the cavity.
Sham's group is concentrating on two directions in the collaboration in this MURI, building logic gates between two spin qubits residing in two separate semiconductor dots in the same neighborhood and logic gates between two qubits, at least one of which is a spin qubit in a dot.
Logic gates between two dots in the same node of a quantum network
In collaboration with Edo Waks of Maryland and Duncan Steel of Michigan, we have completed a design of an optically controlled phase gate between two vertical dots and have prepared a draft for publication. The vertical dots have to be fabricated such that when one dot electron is optically excited, the hole generated can tunnel between the two dots. This creates a Pauli blocking mechanism such that the excited state can return to one computational (ground basis) state of the two spins changing its phase without affecting the phases of the other basis states. The operation returns the two dot spins to their ground state while the tunnel between dots is switched off. This makes the operation in principle scalable even though vertical dots are too limited geographically for scaling. The logic operation would serve well to make the local node of a quantum net work non-exponentially more efficient. Simulation of a simple model shows the operation to be fast (~ 10 ps) with a fidelity of 0.96, neglecting the trion decay (time ~ 1 ns >> 10 ps operation time). To reach the 0.99 threshold, we need improvement in operation and include the trion decay in the fidelity estimate.
In collaboration with Steel's group, Sham's group is also investigating the feasibility of utilizing optically excited interaction between two trions for logic operations on the two spin ground states in two dots.
Logic gates between two nodes
In the submitted paper, we propose a theory of applying two bases for each qubit. The qubit axis in one basis is at an angle from the axis of the same qubit in the other basis. Control swaps on two systems of bases between two qubits can then effect the rotation through the angle between two qubit axes in one locality. The significance is the high precision for small angle rotations which is achievable because the initial and final states are prepared without time constraint. The theory consequence of universal computation with only the Clifford group of operations (involving rotations π/4 and its multiples) would greatly facilitate scalability and would allow simpler experimental demonstrations of fault tolerance without complex error corrections.
We have carried out two different numerical simulations with two slightly different methods by two different students to study the rotation precision by the unitary control error in control swap. We are using the data to understand the error process.
We have used simulation to demonstrate fault tolerance of the controlled swap between non-local bases.
We are designing the dot system in open air and in photonic lattice cavity and waveguide for a logic gate between two distant qubits via the photon qubit.
Our current research effort is focused on controlling and measuring the properties of seminconductor quantum dot (QD) spin states when interacting with optical cavities. Our optical cavities are fabricated by introducing defects into photonic crystals etched in gallium arsenide (GaAs) using electron beam lithography, as shown in Figure 1. These cavities exhibit high quality factors and small mode volumes, enabling them to achieve ultra-strong interactions with atomic systems such as quantum dots. In order to isolate the spin states of a single QD, we apply a magnetic field to lift the degeneracy between the two circularly polarized dipole transitions. The effect of the magnetic field is shown in Figure 2, where the spectrum of a bare QD is measured as s function of magnetic field. The QD emission splits into two branches corresponding to the right and left circularly polarized dipole transitions. These two spin transitions can be sepectively tuned onto the cavity mode as shown in Figure 3. The anti-crossing between the spin transition and the cavity mode shows that we are working in the strong coupling regime of cavity QED. These results are the starting point for a broad range of experiments aimed at transferring quantum coherence between a QD and a photon field.