arXiv subjects

Gerard J. Milburn

Publications and source records attributed to Gerard J. Milburn.

36 records · Page 2Linked to original sources

arXiv2012

Phonon number measurements using single photon opto-mechanics

We describe a system composed of two coupled optical cavity modes with a coupling modulated by a bulk mechanical resonator. In addition, one of the cavity modes is irreversibly coupled to a single photon source. Our scheme is an opto-mechanical realisation of the Jaynes-Cummings model where the qubit is a dual rail optical qubit while the bosonic degree of freedom is a matter degree of freedom realised as the bulk mechanical excitation. We show the possibility of engineering phonon number states of the mechanical oscillator in such a system by computing the conditional state of the mechanics after successive photon counting measurements.

quant-ph↗

arXiv2011

Clocks and Relationalism in the Thermal Time Hypothesis

The Thermal Time Hypotheis (TTH) has been proposed as a general method for identifying a time variable from within background-free theories which do not come equipped with a pre-defined clock variable. Here, we explore some implications of the TTH in an entirely relational context by constructing a protocol for the creation of "thermal clocks" from components of a large but finite quantum mechanical system. The protocol applies locally, in the sense that we do not attempt to construct a single clock describing the evolution of the entire system, but instead we construct clocks which describe the evolution of each subsystem of interest. We find that a consistency condition required for the evolution of our clocks is operationally equivalent to the general relativistic Tolman-Ehrenfest relation for thermal equilibrium in a static gravitational field but without the assumption of gravity or a metric field of any kind.

gr-qc↗

arXiv2010

Simulating quantum effects of cosmological expansion using a static ion trap

We propose a new experimental testbed that uses ions in the collective ground state of a static trap for studying the analog of quantum-field effects in cosmological spacetimes, including the Gibbons-Hawking effect for a single detector in de Sitter spacetime, as well as the possibility of modeling inflationary structure formation and the entanglement signature of de Sitter spacetime. To date, proposals for using trapped ions in analog gravity experiments have simulated the effect of gravity on the field modes by directly manipulating the ions' motion. In contrast, by associating laboratory time with conformal time in the simulated universe, we can encode the full effect of curvature in the modulation of the laser used to couple the ions' vibrational motion and electronic states. This model simplifies the experimental requirements for modeling the analog of an expanding universe using trapped ions and enlarges the validity of the ion-trap analogy to a wide range of interesting cases.

quant-ph↗

arXiv2009

Scalable Quantum Computing based on Spin Qubits in CNT QD

We study experimentally demonstrated single-electron ${}^{12}$C CNT QD with significant spin-orbit interaction as a scalable quantum computer candidate. Both electron spin and orbital angular momentum can serve as a logical qubit for quantum processing. We introduce macroscopic quantum memory for the system in a form of injected either magnetic or spin carrying atomic ensemble into the nanotube. CNT provides with a stable atomic trap in finite temperature and with one-dimensional nuclear spin lattice in an external magnetic field. The electron is coupled to the atomic ensemble through either magnetic or hyperfine interaction. Easy electron and nuclear spin read-out procedure for this system is possible.

quant-ph↗

arXiv2009

Giant Kerr nonlinearities in Circuit-QED

The very small size of optical nonlinearities places wide ranging restrictions on the types of novel physics one can explore. For an ensemble of multi-level systems one can synthesize a large effective optical nonlinearity using quantum coherence effects but such non-linearities are technically extremely challenging to demonstrate at the single atom level. In this work we describe how a single artificial multi-level Cooper Pair Box molecule, interacting with a superconducting microwave coplanar waveguide resonator, when suitably driven, can generate extremely large optical nonlinearities at microwave frequencies, with no associated absorption. We describe how the giant self-Kerr effect can be detected by measuring the second-order correlation function and quadrature squeezing spectrum.

quant-ph↗

arXiv2009

The Jahn-Teller instability in dissipative quantum electromechanical systems

We consider the steady states of a harmonic oscillator coupled so strongly to a two-level system (a qubit) that the rotating wave approximation cannot be made. The Hamiltonian version of this model is known as the $E\otimesβ$ Jahn-Teller model. The semiclassical version of this system exhibits a fixed point bifurcation, which in the quantum model leads to a ground state with substantial entanglement between the oscillator and the qubit. We show that the dynamical bifurcation survives in a dissipative quantum description of the system, amidst an even richer bifurcation structure. We propose two experimental implementations of this model based on superconducting cavities: a parametrically driven nonlinear nanomechanical resonator coupled capacitively to a coplanar microwave cavity and a superconducting junction in the central conductor of a coplanar waveguide.

cond-mat.mes-hall↗

arXiv2007

Decoherence and dissipation of a quantum harmonic oscillator coupled to two-level systems

We derive and analyze the Born-Markov master equation for a quantum harmonic oscillator interacting with a bath of independent two-level systems. This hitherto virtually unexplored model plays a fundamental role as one of the four "canonical" system-environment models for decoherence and dissipation. To investigate the influence of further couplings of the environmental spins to a dissipative bath, we also derive the master equation for a harmonic oscillator interacting with a single spin coupled to a bosonic bath. Our models are experimentally motivated by quantum-electromechanical systems and micron-scale ion traps. Decoherence and dissipation rates are found to exhibit temperature dependencies significantly different from those in quantum Brownian motion. In particular, the systematic dissipation rate for the central oscillator decreases with increasing temperature and goes to zero at zero temperature, but there also exists a temperature-independent momentum-diffusion (heating) rate.

quant-ph↗

arXiv2005

Teleportation via multi-qubit channels

We investigate the problem of teleporting an unknown qubit state to a recipient via a channel of $2Ł$ qubits. In this procedure a protocol is employed whereby $Ł$ Bell state measurements are made and information based on these measurements is sent via a classical channel to the recipient. Upon receiving this information the recipient determines a local gate which is used to recover the original state. We find that the $2^{2Ł}$-dimensional Hilbert space of states available for the channel admits a decomposition into four subspaces. Every state within a given subspace is a perfect channel, and each sequence of Bell measurements projects $2Ł$ qubits of the system into one of the four subspaces. As a result, only two bits of classical information need be sent to the recipient for them to determine the gate. We note some connections between these four subspaces and ground states of many-body Hamiltonian systems, and discuss the implications of these results towards understanding entanglement in multi-qubit systems.

quant-ph↗

arXiv2004

Communicating continuous quantum variables between different Lorentz frames

We show how to communicate Heisenberg-limited continuous (quantum) variables between Alice and Bob in the case where they occupy two inertial reference frames that differ by an unknown Lorentz boost. There are two effects that need to be overcome: the Doppler shift and the absence of synchronized clocks. Furthermore, we show how Alice and Bob can share Doppler-invariant entanglement, and we demonstrate that the protocol is robust under photon loss.

quant-ph↗

arXiv2004

A practical scheme for error control using feedback

We describe a scheme for quantum error correction that employs feedback and weak measurement rather than the standard tools of projective measurement and fast controlled unitary gates. The advantage of this scheme over previous protocols (for example Ahn et. al, PRA, 65, 042301 (2001)), is that it requires little side processing while remaining robust to measurement inefficiency, and is therefore considerably more practical. We evaluate the performance of our scheme by simulating the correction of bit-flips. We also consider implementation in a solid-state quantum computation architecture and estimate the maximal error rate which could be corrected with current technology.

quant-ph↗

arXiv2002

Entanglement of two-mode Bose-Einstein condensates

We investigate the entaglement characteristics of two general bimodal Bose-Einstein condensates - a pair of tunnel-coupled Bose-Einstein condensates and the atom-molecule Bose-Einstein condensate. We argue that the entanglement is only physically meaningful if the system is viewed as a bipartite system, where the subsystems are the two modes. The indistinguishibility of the particles in the condensate means that the atomic constituents are physically inaccessible and thus the degree of entanglement between individual particles, unlike the entanglement between the modes, is not experimentally relevant so long as the particles remain in the condensed state. We calculate the entanglement between the modes for the exact ground state of the two bimodal condensates and consider the dynamics of the entanglement in the tunnel-coupled case.

quant-ph↗

arXiv2002

Quantum Technology: The Second Quantum Revolution

We are currently in the midst of a second quantum revolution. The first quantum revolution gave us new rules that govern physical reality. The second quantum revolution will take these rules and use them to develop new technologies. In this review we discuss the principles upon which quantum technology is based and the tools required to develop it. We discuss a number of examples of research programs that could deliver quantum technologies in coming decades including; quantum information technology, quantum electromechanical systems, coherent quantum electronics, quantum optics and coherent matter technology.

quant-ph↗

arXiv2002

Lorentz Invariance of Entanglement

We study the transformation of maximally entangled states under the action of Lorentz transformations in a fully relativistic setting. By explicit calculation of the Wigner rotation, we describe the relativistic analog of the Bell states as viewed from two inertial frames moving with constant velocity with respect to each other. Though the finite dimensional matrices describing the Lorentz transformations are non-unitary, each single particle state of the entangled pair undergoes an effective, momentum dependent, local unitary rotation, thereby preserving the entanglement fidelity of the bipartite state. The details of how these unitary transformations are manifested are explicitly worked out for the Bell states comprised of massive spin 1/2 particles and massless photon polarizations. The relevance of this work to non-inertial frames is briefly discussed.

quant-ph↗

arXiv2001

Dynamics of a mesoscopic qubit under continuous quantum measurement

We present the conditional quantum dynamics of an electron tunneling between two quantum dots subject to a measurement using a low transparency point contact or tunnel junction. The double dot system forms a single qubit and the measurement corresponds to a continuous in time readout of the occupancy of the quantum dot. We illustrate the difference between conditional and unconditional dynamics of the qubit. The conditional dynamics is discussed in two regimes depending on the rate of tunneling through the point contact: quantum jumps, in which individual electron tunneling current events can be distinguished, and a diffusive dynamics in which individual events are ignored, and the time-averaged current is considered as a continuous diffusive variable. We include the effect of inefficient measurement and the influence of the relative phase between the two tunneling amplitudes of the double dot/point contact system.

cond-mat.mes-hall↗

arXiv2001

Conditional quantum evolution induced by continuous measurement for a mesoscopic qubit

We consider the problem of an electron tunneling between two coupled quantum dots, a two-state quantum system (qubit), using a low-transparency point contact (PC) or tunnel junction as a detector continually measuring the position of the electron. We focus on the qubit dynamics conditioned on a particular realization of the actual measured current through the PC device. We illustrate the conditional evolutions by numerical simulations. The different behaviors between unconditional and conditional evolutions are demonstrated. The conditional qubit dynamics evolving from quantum jumps to quantum diffusion is presented.

cond-mat.mes-hall↗

arXiv1999

Qutrit Entanglement

We consider the separability of various joint states for N qutrits. We derive two results: (i) the separability condition for a two-qutrit state that is a mixture of the maximally mixed state and a maximally entangled state (such a state is a generalization of the Werner state for two qubits); (ii) upper and lower bounds on the size of the neighborhood of separable states surrounding the maximally mixed state for N qutrits.

quant-ph↗

arXiv1998

Method of quantum computation with ``hot'' trapped ions

We present a novel method of performing quantum logic gates in trapped ion quantum computers which does not require the ions to be cooled down to their vibrational center of mass (CM) mode ground state. Our scheme employs adiabatic passages and the conditional phase shift first investigated by D'Helon and Milburn (C.~D'Helon and G.J.~Milburn, Phys. Rev. A {\bf 54}, 5141 (1996)).

quant-ph↗

arXiv1998

Quantum State Protection in Cavities

We show how an initially prepared quantum state of a radiation mode in a cavity can be preserved for a long time using a feedback scheme based on the injection of appropriately prepared atoms. We present a feedback scheme both for optical cavities, which can be continuously monitored by a photodetector, and for microwave cavities, which can be monitored only indirectly via the detection of atoms that have interacted with the cavity field. We also discuss the possibility of applying these methods for decoherence control in quantum information processing.

quant-ph↗