Denzil Rodrigues
| Personal Details | Publications |
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Research Associate School of Physics & Astronomy, Faculty of Science Role(s): Researcher |
Staff listing |
| Contact | |
| Room C18 Mathematics and Physics University Park NG7 2RD T: 0115 9515130 F: 0115 9515180 denzil.rodrigues@nottingham.ac.uk |
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Expertise summary |
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| My PhD involved the study of both condensed matter physics and quantum information theory, and focussed on the application of condensed matter theory to superconducting charge qubits. In a superconducting charge qubit, a small superconducting island is connected to two superconducting leads through Josephson tunnel junctions. The island is small enough that the number of Cooper pairs on the island is restricted to taking one of two values. These two values represent the logical basis of the qubit. For a large Josephson junction, the quantum mechanical description of the junction can be used to derive a classical set of equations of motion for the superconducting phase. Previous theoretical descriptions of small Josephson junctions have taken this macroscopic description, and then applied a cannonical quantisation to produce the `quantised Josephson equation.' This, then, is a quantisation of a classical set of equations derived in turn from underlying quantum mechanical laws. My research involved finding a description directly derived from a microscopic theory, and calculating corrections to the existing theory. Specifically, I investigated how the behaviour of a superconducting island changes as a function of size. I considered a simplified form of the superconducting Hamiltonian in which the single-electron energy levels are all taken to be equal. The Hamiltonian of an island then corresponds directly to that of a large, quantum spin, and can be solved exactly, rather than just in the mean field limit. This allowed a simple and rigorous derivation of the phase-basis Hamiltonian that is commonly used in describing Josephson junction systems, as well as corrections to this due to the finite size of the island. The spin representation means that the behaviour of a superconductor is analogous to that of a harmonic oscillator, and several of the effects occurring in quantum optics should therefore have analogies in the behaviour of superconducting circuits. I investigated analogues of radiation trapping and superradiance in arrays of Josephson systems which indicate quantum behaviour without recourse to entanglement measurements. I also investigated a superconducting analogue of revival. The state of a Cooper pair box coupled to a reservoir apparently decoheres and then revives at a later time. Studies of two entangled boxes show a similar decoherence and revival of entanglement. After completing my PhD in 2003 I worked on electromagnetically induced transition (EIT) for use in optical qubits. In EIT, an ensemble of atoms can be used to give a non-linear coupling (a Kerr non-linearity) between two photon modes, which can then be used to perform a qubit gate operation. During my three months at H.P. I performed a detailed analysis of the efficiency of this method for both single qubit and two qubit gates. At the beginning of 2004 I accepted a position as a Research Associate in Andrew Armour's group at the University of Nottingham, and began my work on nanoelectromechanical systems (NEMS). In these systems, nanomechanical resonators (with dimensions on the order of 100nm) are coupled to mesoscopic conductors. These can then be used to measure the position of the resonators. However, the conductors also have a significant back-action effect on the resonator and so an understanding of these systems requires a description that captures the interplay between the mechanical and electronic degrees of freedom. One particularly dramatic effect that the conductor can have is to damp the oscillations of the resonator. Armour, Blencowe and Zhang showed, using a classical master equation description, that an SET coupled to a resonator acts as an additional thermal bath for the resonator, with both damping and heating effects. This damping in a classical system was surprising, as previous studies of NEMS had described an intrinsically quantum mechanical damping that would not be expected in a purely classical system. My work has shown that the classical damping arises from a subtle interplay between the electronic and mechanical degrees of freedom. In the classical limit, the tunnelling through the SET occurs at a much faster rate than the oscillations of the resonator, and so the average charge on the SET "follows" the position of the resonator as it oscillates. This charge then acts as an additional force on the resonator, leading to a frequency shift, and the "lag" in the charge as it tries to follow the resonator leads to the damping effect. This separation of timescales allows the derivation of a Fokker-Planck equation for the resonator alone. I have used a classical description of the combined SET-resonator system to study analytically the zero-frequency current noise through the SET. We found that the current noise diverges as the frequency of the oscillator is reduced compared to the tunnelling through the SET. We also found that the current noise is close to linear in the SET-resonator coupling, which is unexpected as linear response theory predicts no linear term. We have shown that both these effects are due to the fact that the SET acts as an effective thermal bath on the resonator. My most recent work has focussed on the two very different descriptions of NEMS present in the literature that have seemingly incompatible features. One approach is to describe the resonator and measuring device by a quantum mechanical Hamiltonian, and then derive a master equation for the resonator. This approach led to a damping that is proportional to the tunnelling rate of electrons through the measuring device, and that appeared to operate by exchange of phonons during the tunnelling. A contrasting approach is to describe the system phenomenologically, using classical equations. This approach led to a damping inversely proportional to the tunnelling rate, and describes the damping mechanism as due to the response of the measuring device to the resonator. From a microscopic quantum description, I showed that the previous approaches can be rederived as the limits of a single equation . In the limit of fast oscillator motion, the rotating wave approximation applies, and the `quantum' description is recaptured. In the limit of slow oscillator motion, the classical description is rederived. In fact, I have shown that for high and intermediate bias voltages, the behaviour is essentially classical for all resonator frequencies, even though a quantum description has previously been used. This work not only provides insight into damping mechanisms in NEMS, but has linked two diverging approaches in the literature, and clarified when a quantum mechanical description is required. | |||
Lay summary |
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| Dr Rodrigues is currently working in the the field of Nano-electromechanics or NEMS, an emerging technology where tiny machines (such as vibrating beams) are built onto silicon chips in the same way as electronics are miniaturised on computer chips. As well as having the same advantages as computer chips, such as reliability, small size and low cost, having mechanical devices on a chip instead of just electronics leads to a wide range of completely novel applications, ranging from optical switches, to car airbag sensors, to weighing scales sensitive enough to measure the mass of a single DNA molecule. However, as well as offering many new technologies, NEMS can also cast light on important physical questions, such as the quantum-classical transition, the limits of measurement and how non-classical states can be observed. Dr Rodrigues is also interested in quantum computation, and in particular how superconducting devices can be constructed that can be used as qubits. | |||
Media summary |
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| Dr Rodrigues is currently working in the the field of Nano-electromechanics or NEMS, an emerging technology where tiny machines (such as vibrating beams) are built onto silicon chips in the same way as electronics are miniaturised on computer chips. As well as having the same advantages as computer chips, such as reliability, small size and low cost, having mechanical devices on a chip instead of just electronics leads to a wide range of completely novel applications, ranging from optical switches, to car airbag sensors, to weighing scales sensitive enough to measure the mass of a single DNA molecule. However, as well as offering many new technologies, NEMS can also cast light on important physical questions, such as the quantum-classical transition, the limits of measurement and how non-classical states can be observed. Recent work has included a study of the zero-frequency noise in a classical single electron transisto-resonator system, and a detailed investigation into the origin of detector-induced damping in this device, in both a classical and a quantum description. Dr Rodrigues is also interested in quantum computation, and in particular how superconducting devices can be constructed that can be used as qubits. | |||
