Quantum Electro Mechanics
Introduction
Efforts in the Roukes Milli-Kelvin Lab are currently focused on the emerging field of quantum electromechanical systems (QEMS) ( , ), with particular attention devoted to the integration of superconducting quantum electronics in VHF and UHF nanoelectromechanical systems (NEMS). The natural compatibility of NEMS and nanoscale electronics has motivated many proposals to exploit the quantum properties of devices like the Cooper-pair box (CPB) qubit or the superconducting single-electron transistor (SSET) for the sake of quantum-limited nanomechanical transduction and control. It is thought they will ultimately allow for the observation of NEMS’ superposition states, Fock states, and other non-classical states of matter. While nanoscopic in scale, our NEMS modes consist of billions of atoms and can be characterized by a single degree-of-freedom, e.g. displacement or velocity of a cantilever’s tip or the center-of-mass of a doubly-clamped resonator. Engineering quantum states of such “macroscopic” variables would constitute a milestone in quantum experiments and provide a new regime in which to study the physics of quantum measurement and decoherence. Towards this end, we are presently engaged in a collaboration with Keith Schwab (Cornell) and Pierre Echternach (Jet Propulsion Laboratory, Caltech), investigating, for the first time ever, the dispersive coupling between a NEMS resonator and CPB qubit.
Efforts in the Roukes Milli-Kelvin Lab are currently focused on the emerging field of quantum electromechanical systems (QEMS) ( , ), with particular attention devoted to the integration of superconducting quantum electronics in VHF and UHF nanoelectromechanical systems (NEMS). The natural compatibility of NEMS and nanoscale electronics has motivated many proposals to exploit the quantum properties of devices like the Cooper-pair box (CPB) qubit or the superconducting single-electron transistor (SSET) for the sake of quantum-limited nanomechanical transduction and control. It is thought they will ultimately allow for the observation of NEMS’ superposition states, Fock states, and other non-classical states of matter. While nanoscopic in scale, our NEMS modes consist of billions of atoms and can be characterized by a single degree-of-freedom, e.g. displacement or velocity of a cantilever’s tip or the center-of-mass of a doubly-clamped resonator. Engineering quantum states of such “macroscopic” variables would constitute a milestone in quantum experiments and provide a new regime in which to study the physics of quantum measurement and decoherence. Towards this end, we are presently engaged in a collaboration with Keith Schwab (Cornell) and Pierre Echternach (Jet Propulsion Laboratory, Caltech), investigating, for the first time ever, the dispersive coupling between a NEMS resonator and CPB qubit.
Figure 1:
SEM image of a first generation sample for measuring the
dispersive interaction between a CPB qubit and NEMS resonator.
Lithography by
Background
Recent progress by Roukes group members in the engineering and measurement of UHF NEMS (3) along with the demonstration of SET-based NEMS transduction schemes by the Cleland and Schwab groups ( 4, 5, 6) has provided the fuel for our present research efforts. Nanomechanical frequencies in excess of 1 GHz are possible (3), and 10-100’s MHz are routine, making viable the use of standard cryogenic refrigeration to cool individual nanomechanical modes to low thermal occupation numbers where is Boltzman’s constant, T is the temperature of the mode, and h/2pi is the frequency of the resonator mode, and is Planck’s constant. For example, a 1 GHz resonator mode would have a thermal occupation number nth ~ 1 at T=50 mK, which is a temperature that is routinely achieved using dilution refrigeration- the world record to-date is held by the Schwab group, who measured a thermal occupation of nth ~ 25 for a 21 MHz NEMS mode (5). At such low occupations, where the thermal fluctuations kBT in the nanoresonator’s energy are comparable to the nanoresonator’s energy quanta , it should become much easier to observe the quantum nature of the resonator (7, 8).
But this begs the question of how to actually measure the quantum nature of the NEMS. One possible set of measurement tools include superconducting electronics like the CPB qubit (9), flux (10) and phase (11) qubits or the SSET (12) whose properties are dominated (in the case of the CPB) or in large part influenced (in the case of the SSET) by quantum mechanics. In fact, SSET’s have been operated near the quantum limit for continuous, linear displacement detection (4,5), even allowing for the observation of the influence of the SSET’s quantum noise on the behavior of the NEMS (5). Displacement detection with the SSET could ultimately lead to the production of ultra-cold NEMS modes (13), or even “squeezed” NEMS states (14). However the observation of a nanoresonator existing in a superposition of position states (15) or undergoing a quantum jump in energy (16,17) might require coupling to quantum mechanically “coherent” systems like the CPB, flux or phase qubits. Because of the close similarity in terms of size scale and engineering, between, for example, the SSET and CPB, the success of the initial SSET/NEMS experiments bodes very well for the possibility of eventually entangling a NEMS and solid state qubit. Our initial results measuring the dispersive interaction between a nanoresonator and CPB qubit are beginning to substantiate this assertion.
Recent progress by Roukes group members in the engineering and measurement of UHF NEMS (3) along with the demonstration of SET-based NEMS transduction schemes by the Cleland and Schwab groups ( 4, 5, 6) has provided the fuel for our present research efforts. Nanomechanical frequencies in excess of 1 GHz are possible (3), and 10-100’s MHz are routine, making viable the use of standard cryogenic refrigeration to cool individual nanomechanical modes to low thermal occupation numbers where is Boltzman’s constant, T is the temperature of the mode, and h/2pi is the frequency of the resonator mode, and is Planck’s constant. For example, a 1 GHz resonator mode would have a thermal occupation number nth ~ 1 at T=50 mK, which is a temperature that is routinely achieved using dilution refrigeration- the world record to-date is held by the Schwab group, who measured a thermal occupation of nth ~ 25 for a 21 MHz NEMS mode (5). At such low occupations, where the thermal fluctuations kBT in the nanoresonator’s energy are comparable to the nanoresonator’s energy quanta , it should become much easier to observe the quantum nature of the resonator (7, 8).
But this begs the question of how to actually measure the quantum nature of the NEMS. One possible set of measurement tools include superconducting electronics like the CPB qubit (9), flux (10) and phase (11) qubits or the SSET (12) whose properties are dominated (in the case of the CPB) or in large part influenced (in the case of the SSET) by quantum mechanics. In fact, SSET’s have been operated near the quantum limit for continuous, linear displacement detection (4,5), even allowing for the observation of the influence of the SSET’s quantum noise on the behavior of the NEMS (5). Displacement detection with the SSET could ultimately lead to the production of ultra-cold NEMS modes (13), or even “squeezed” NEMS states (14). However the observation of a nanoresonator existing in a superposition of position states (15) or undergoing a quantum jump in energy (16,17) might require coupling to quantum mechanically “coherent” systems like the CPB, flux or phase qubits. Because of the close similarity in terms of size scale and engineering, between, for example, the SSET and CPB, the success of the initial SSET/NEMS experiments bodes very well for the possibility of eventually entangling a NEMS and solid state qubit. Our initial results measuring the dispersive interaction between a nanoresonator and CPB qubit are beginning to substantiate this assertion.
Dispersive Interaction Between a
Nanoresonator and CPB Qubit
While other variants have been proposed, here the interaction between the NEMS and CPB qubit is achieved via electrostatic coupling, Figure 1 and Figure 2. In this scenario, the capacitance between the CPB island and a nearby, metallized nanoresonator is modulated through the displacement of the resonator about its equilibrium position. If a DC voltage bias is applied to the resonator, modulation of the capacitance results in modulation of the potential of the CPB island. For typical parameters, the interaction is characterized as dispersive, meaning that one should observe a renormalization of the frequency of the NEMS that is determined by the CPB state (16). A NEMS-dependent augmentation of the CPB state should also arise, yielding the possibility of performing a “non-destructive” measurement of the NEMS’ Fock state. However, given the sensitive nanomechanical detection schemes at our disposal, we have decided to initially use the
frequency of the NEMS to read-out the state of the CPB and in the process study the underlying interaction.
Continued>>
While other variants have been proposed, here the interaction between the NEMS and CPB qubit is achieved via electrostatic coupling, Figure 1 and Figure 2. In this scenario, the capacitance between the CPB island and a nearby, metallized nanoresonator is modulated through the displacement of the resonator about its equilibrium position. If a DC voltage bias is applied to the resonator, modulation of the capacitance results in modulation of the potential of the CPB island. For typical parameters, the interaction is characterized as dispersive, meaning that one should observe a renormalization of the frequency of the NEMS that is determined by the CPB state (16). A NEMS-dependent augmentation of the CPB state should also arise, yielding the possibility of performing a “non-destructive” measurement of the NEMS’ Fock state. However, given the sensitive nanomechanical detection schemes at our disposal, we have decided to initially use the
frequency of the NEMS to read-out the state of the CPB and in the process study the underlying interaction.
Continued>>
Figure 2:
Schematic of Nanoresonator coupled to CPB.
Figure
3:
Nanomechanical frequency shift
Dfo versus CPB gate voltage ncpb
(Vcpb in units of Cooper-pairs, 2e) for the CPB
in the excited state (Y+)
and ground state (Y-).
Estimates are for a 60 MHz nanoresonator coupled to the CPB
with an interaction strength of 1.5 MHz.