Using the conventional Bohr interpretation of a ≪quantum measurement≫ as an interaction between a... more Using the conventional Bohr interpretation of a ≪quantum measurement≫ as an interaction between a ≪quantum object≫ and a ≪classical apparatus≫, we consider the voltage-current characteristics of a singly connected weak link. We employ a well-known electrical engineering model using a shunt resistor. The equations are described in a simple Lagrangian form eliminating the need to consider explicitly the dynamics of the dissipative degrees of freedom internal to the resistor.
In this paper we demonstrate that the energy level structure of ultra small capacitance SQUID rin... more In this paper we demonstrate that the energy level structure of ultra small capacitance SQUID rings can be probed adiabatically at radio frequency using both dynamical and quasistatic reactive techniques.
ABSTRACT Using a quantum mechanical model for a frictionless superconducting quantum interference... more ABSTRACT Using a quantum mechanical model for a frictionless superconducting quantum interference device ring subjected to a time varying external magnetic flux we solve the time-dependent Schrödinger equation for the ring and calculate the time-averaged energy and screening current expectation values. We demonstrate by computation that (subject to constraints on the applied field frequency and amplitude) the ring can be treated as a two level system. We also show that for certain regions of the bias flux, the time-averaged energy expectation value appears to jump between the time-averaged energies of the adiabatic ground and first excited states of the ring.
Summary: We discuss the behaviour of a superconducting weak link ring coupled to a radio frequenc... more Summary: We discuss the behaviour of a superconducting weak link ring coupled to a radio frequency tank circuit. We show that with the weak link acting quantum mechanically to connect different winding number states of the ring together two limiting regimes ofbehaviour are ...
We consider the dynamical behavior of a coupled SQUID ring-tank circuit system when the ring is i... more We consider the dynamical behavior of a coupled SQUID ring-tank circuit system when the ring is in its quantum mechanical ground state. As we show, the underlying quantum evolution of the ring generates a non-linear dynamics in the classical tank circuit. In this sense the SQUID ring-tank circuit is a model system for studying the quantum-classical interface.
In this paper we describe very unusual paired bifurcations which can appear in the resonance curv... more In this paper we describe very unusual paired bifurcations which can appear in the resonance curve of a coupled SQUID ring-radio frequency (rf) tank circuit system when the rf flux at the ring is comparable to CJ, (= h/2e). We demonstrate that the position of these bistabilities is controlled by the static magnetic flux @ xStat applied to the ring, with simple bistable regions being observed on the lower or upper side of the resonance when (for n integer) &,,, is close to n@, or (n + l/2) Go, respectively. More interestingly, we show that for values of Qx close to (PI f l/4) Q0 this resonance exhibits bistability on both its lower and upper sides. We discuss this very unusual phenomenon in terms of the non-linear equation of motion for the coupled system. @ 1997 Elsevier Science B.V.
Outline • Background to Electric Potential Sensor (EPS) technology • Performance as non-contact v... more Outline • Background to Electric Potential Sensor (EPS) technology • Performance as non-contact voltage sensor •Performance as non-contact electric field sensor • Applications • Array imaging 1-D and 2-D • Conclusions
We discuss coherent oscillations in the quantum potential view of quantum mechanics, giving examp... more We discuss coherent oscillations in the quantum potential view of quantum mechanics, giving examples for both a superposition of “position” states, and a superposition of “momentum” states.
We discuss the time taken for a particle to pass through a classically forbidden barrier in the q... more We discuss the time taken for a particle to pass through a classically forbidden barrier in the quantum potential approach to quantum mechanics.
We discuss the response of a superconducting weak-link ring to externally applied adiabatic noise... more We discuss the response of a superconducting weak-link ring to externally applied adiabatic noise and show that this can be used as a probe of the low-lying energy eigenstates of the ring. We compare the observable consequences of this with new experimental results.
This paper considers the behavior of a model persistent current qubit in the presence of a time-d... more This paper considers the behavior of a model persistent current qubit in the presence of a time-dependent electromagnetic field. A semi-classical approximation for the electromagnetic field is used to solve the time- dependent Schrodinger equation (TDSE) for the qubit, which is treated as a macroscopic quantum object. The qubit is describe3d by a Hamiltonian involving the enclosed magnetic flux (Phi) and the electric displacement flux Q, which obey the quantum mechanical commutation relation. The paper includes a brief summary of recent work on quantum mechanical coherence in persistent current circuits, and the solution of the TDSE in superconducting rings. Of particular interest is the emergence of strongly non-perturbative behavior that corresponds to transitions between the energy levels of the qubit. These transitions are due to the strong coupling between the electromagnetic fields and the superconducting condensate and can appear at frequencies predicted by conventional methods based on perturbations around the energy eigenstate of the time-independent system. The relevance of these non-perturbative processes to the operation of quantum logic gates based on superconducting circuits and the effect of the resultant non linearities on the environmental degrees of freedom coupled to the qubit are considered.
In this paper we present experimental data on the frequency domain response of a SQUID ring (a Jo... more In this paper we present experimental data on the frequency domain response of a SQUID ring (a Josephson weak link enclosed by a thick superconducting ring) coupled to a radio frequency (rf) tank circuit resonator. We show that with the ring weakly hysteretic the resonance lineshape of this coupled system can display opposed fold bifurcations that appear to touch (pinch off). We demonstrate that for appropriate circuit parameters these pinch off lineshapes exist as solutions of the non-linear equations of motion for the system.
ABSTRACT In this paper, we discuss the nonlinear behavior of a model rf superconducting quantum-i... more ABSTRACT In this paper, we discuss the nonlinear behavior of a model rf superconducting quantum-interference-device magnetometer consisting of a macroscopic quantum object which is coupled reactively to a linear classical oscillator. We demonstrate that chaotic solutions can be found in the oscillator for the ground and first excited states of the quantum object over a wide range of parameters, including those relevant to experimental systems.
ABSTRACT In this paper we consider from a theoretical viewpoint the dynamical behavior of a super... more ABSTRACT In this paper we consider from a theoretical viewpoint the dynamical behavior of a superconducting-quantum-interference-device ring (a single Josephson weak link enclosed by a thick superconducting ring) in its ground state when coupled inductively to a radio frequency (rf) tank circuit resonator. We show that this simple system, when strongly driven at rf, displays a rich nonlinear dynamical structure, including unusual fold bifurcations and chaos.
In this paper we show that the radio frequency (rf) dynamical characteristics of a very strongly ... more In this paper we show that the radio frequency (rf) dynamical characteristics of a very strongly hysteretic SQUID ring, coupled to an rf tank circuit resonator, display relaxation oscillations. We demonstrate that the the overall form of these characteristics, together with the relaxation oscillations, can be modelled accurately by solving the quasi-classical non-linear equations of motion for the system. We suggest that in these very strongly hysteretic regimes SQUID ring-resonator systems may find application in novel logic and memory devices. PACS numbers: 85.25.Dq, 74.50. + r
We consider the dynamical behavior of a strongly hysteretic SQUID ring coupled to a radio frequen... more We consider the dynamical behavior of a strongly hysteretic SQUID ring coupled to a radio frequency resonator. By experiment we show that this system can display novel multiple level structures in its rf voltage-current characteristics which are solutions of the nonlinear equations of motion describing the system.
In this paper we consider the modulation of a SQUID ring (a Josephson weak link enclosed by a thi... more In this paper we consider the modulation of a SQUID ring (a Josephson weak link enclosed by a thick superconducting ring) by an external electromagnetic (em) field for the case where the ring remains adiabatically in its ground state. We demonstrate that very good agreement can be found between experimental modulation data and the results predicted theoretically by solving the time-dependent Schrödinger equation for the ring-em-field system. We also show that the non-linear dynamical coupling between the ring and an external resonant circuit can influence the exact form of the modulation. Again we find consistent agreement between experiment and theory.
We consider a model weak link, an ultra-small capacitor subject to tunnelling, to ohmic dissipati... more We consider a model weak link, an ultra-small capacitor subject to tunnelling, to ohmic dissipation and fed with an external displacement current. The framework we employ is the new approach of quantum state diffusion, which treats individual open quantum systems as well as being able to generate the conventional ensemble averages. We show how evidence for archetypal quantum behaviour (coherent oscillations) and archetypal classical behaviour (chaos) arises, for weak links whose parameters are related by a rather modest scaling. Interestingly, the quantum behaviour can arise for a weak link with intrinsic parameter values such that it could exhibit chaos, if it were a purely classical device.
Using the conventional Bohr interpretation of a ≪quantum measurement≫ as an interaction between a... more Using the conventional Bohr interpretation of a ≪quantum measurement≫ as an interaction between a ≪quantum object≫ and a ≪classical apparatus≫, we consider the voltage-current characteristics of a singly connected weak link. We employ a well-known electrical engineering model using a shunt resistor. The equations are described in a simple Lagrangian form eliminating the need to consider explicitly the dynamics of the dissipative degrees of freedom internal to the resistor.
In this paper we demonstrate that the energy level structure of ultra small capacitance SQUID rin... more In this paper we demonstrate that the energy level structure of ultra small capacitance SQUID rings can be probed adiabatically at radio frequency using both dynamical and quasistatic reactive techniques.
ABSTRACT Using a quantum mechanical model for a frictionless superconducting quantum interference... more ABSTRACT Using a quantum mechanical model for a frictionless superconducting quantum interference device ring subjected to a time varying external magnetic flux we solve the time-dependent Schrödinger equation for the ring and calculate the time-averaged energy and screening current expectation values. We demonstrate by computation that (subject to constraints on the applied field frequency and amplitude) the ring can be treated as a two level system. We also show that for certain regions of the bias flux, the time-averaged energy expectation value appears to jump between the time-averaged energies of the adiabatic ground and first excited states of the ring.
Summary: We discuss the behaviour of a superconducting weak link ring coupled to a radio frequenc... more Summary: We discuss the behaviour of a superconducting weak link ring coupled to a radio frequency tank circuit. We show that with the weak link acting quantum mechanically to connect different winding number states of the ring together two limiting regimes ofbehaviour are ...
We consider the dynamical behavior of a coupled SQUID ring-tank circuit system when the ring is i... more We consider the dynamical behavior of a coupled SQUID ring-tank circuit system when the ring is in its quantum mechanical ground state. As we show, the underlying quantum evolution of the ring generates a non-linear dynamics in the classical tank circuit. In this sense the SQUID ring-tank circuit is a model system for studying the quantum-classical interface.
In this paper we describe very unusual paired bifurcations which can appear in the resonance curv... more In this paper we describe very unusual paired bifurcations which can appear in the resonance curve of a coupled SQUID ring-radio frequency (rf) tank circuit system when the rf flux at the ring is comparable to CJ, (= h/2e). We demonstrate that the position of these bistabilities is controlled by the static magnetic flux @ xStat applied to the ring, with simple bistable regions being observed on the lower or upper side of the resonance when (for n integer) &,,, is close to n@, or (n + l/2) Go, respectively. More interestingly, we show that for values of Qx close to (PI f l/4) Q0 this resonance exhibits bistability on both its lower and upper sides. We discuss this very unusual phenomenon in terms of the non-linear equation of motion for the coupled system. @ 1997 Elsevier Science B.V.
Outline • Background to Electric Potential Sensor (EPS) technology • Performance as non-contact v... more Outline • Background to Electric Potential Sensor (EPS) technology • Performance as non-contact voltage sensor •Performance as non-contact electric field sensor • Applications • Array imaging 1-D and 2-D • Conclusions
We discuss coherent oscillations in the quantum potential view of quantum mechanics, giving examp... more We discuss coherent oscillations in the quantum potential view of quantum mechanics, giving examples for both a superposition of “position” states, and a superposition of “momentum” states.
We discuss the time taken for a particle to pass through a classically forbidden barrier in the q... more We discuss the time taken for a particle to pass through a classically forbidden barrier in the quantum potential approach to quantum mechanics.
We discuss the response of a superconducting weak-link ring to externally applied adiabatic noise... more We discuss the response of a superconducting weak-link ring to externally applied adiabatic noise and show that this can be used as a probe of the low-lying energy eigenstates of the ring. We compare the observable consequences of this with new experimental results.
This paper considers the behavior of a model persistent current qubit in the presence of a time-d... more This paper considers the behavior of a model persistent current qubit in the presence of a time-dependent electromagnetic field. A semi-classical approximation for the electromagnetic field is used to solve the time- dependent Schrodinger equation (TDSE) for the qubit, which is treated as a macroscopic quantum object. The qubit is describe3d by a Hamiltonian involving the enclosed magnetic flux (Phi) and the electric displacement flux Q, which obey the quantum mechanical commutation relation. The paper includes a brief summary of recent work on quantum mechanical coherence in persistent current circuits, and the solution of the TDSE in superconducting rings. Of particular interest is the emergence of strongly non-perturbative behavior that corresponds to transitions between the energy levels of the qubit. These transitions are due to the strong coupling between the electromagnetic fields and the superconducting condensate and can appear at frequencies predicted by conventional methods based on perturbations around the energy eigenstate of the time-independent system. The relevance of these non-perturbative processes to the operation of quantum logic gates based on superconducting circuits and the effect of the resultant non linearities on the environmental degrees of freedom coupled to the qubit are considered.
In this paper we present experimental data on the frequency domain response of a SQUID ring (a Jo... more In this paper we present experimental data on the frequency domain response of a SQUID ring (a Josephson weak link enclosed by a thick superconducting ring) coupled to a radio frequency (rf) tank circuit resonator. We show that with the ring weakly hysteretic the resonance lineshape of this coupled system can display opposed fold bifurcations that appear to touch (pinch off). We demonstrate that for appropriate circuit parameters these pinch off lineshapes exist as solutions of the non-linear equations of motion for the system.
ABSTRACT In this paper, we discuss the nonlinear behavior of a model rf superconducting quantum-i... more ABSTRACT In this paper, we discuss the nonlinear behavior of a model rf superconducting quantum-interference-device magnetometer consisting of a macroscopic quantum object which is coupled reactively to a linear classical oscillator. We demonstrate that chaotic solutions can be found in the oscillator for the ground and first excited states of the quantum object over a wide range of parameters, including those relevant to experimental systems.
ABSTRACT In this paper we consider from a theoretical viewpoint the dynamical behavior of a super... more ABSTRACT In this paper we consider from a theoretical viewpoint the dynamical behavior of a superconducting-quantum-interference-device ring (a single Josephson weak link enclosed by a thick superconducting ring) in its ground state when coupled inductively to a radio frequency (rf) tank circuit resonator. We show that this simple system, when strongly driven at rf, displays a rich nonlinear dynamical structure, including unusual fold bifurcations and chaos.
In this paper we show that the radio frequency (rf) dynamical characteristics of a very strongly ... more In this paper we show that the radio frequency (rf) dynamical characteristics of a very strongly hysteretic SQUID ring, coupled to an rf tank circuit resonator, display relaxation oscillations. We demonstrate that the the overall form of these characteristics, together with the relaxation oscillations, can be modelled accurately by solving the quasi-classical non-linear equations of motion for the system. We suggest that in these very strongly hysteretic regimes SQUID ring-resonator systems may find application in novel logic and memory devices. PACS numbers: 85.25.Dq, 74.50. + r
We consider the dynamical behavior of a strongly hysteretic SQUID ring coupled to a radio frequen... more We consider the dynamical behavior of a strongly hysteretic SQUID ring coupled to a radio frequency resonator. By experiment we show that this system can display novel multiple level structures in its rf voltage-current characteristics which are solutions of the nonlinear equations of motion describing the system.
In this paper we consider the modulation of a SQUID ring (a Josephson weak link enclosed by a thi... more In this paper we consider the modulation of a SQUID ring (a Josephson weak link enclosed by a thick superconducting ring) by an external electromagnetic (em) field for the case where the ring remains adiabatically in its ground state. We demonstrate that very good agreement can be found between experimental modulation data and the results predicted theoretically by solving the time-dependent Schrödinger equation for the ring-em-field system. We also show that the non-linear dynamical coupling between the ring and an external resonant circuit can influence the exact form of the modulation. Again we find consistent agreement between experiment and theory.
We consider a model weak link, an ultra-small capacitor subject to tunnelling, to ohmic dissipati... more We consider a model weak link, an ultra-small capacitor subject to tunnelling, to ohmic dissipation and fed with an external displacement current. The framework we employ is the new approach of quantum state diffusion, which treats individual open quantum systems as well as being able to generate the conventional ensemble averages. We show how evidence for archetypal quantum behaviour (coherent oscillations) and archetypal classical behaviour (chaos) arises, for weak links whose parameters are related by a rather modest scaling. Interestingly, the quantum behaviour can arise for a weak link with intrinsic parameter values such that it could exhibit chaos, if it were a purely classical device.
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Papers by Helen Prance