Quantum driving and work.

Quantum mechanics dictates that a continuous measurement of the position of an object imposes a random quantum back-action (QBA) perturbation on its momentum. This randomness translates with time into position uncertainty, thus leading to the well known uncertainty on the measurement of motion. As a consequence of this randomness, and in accordance with the Heisenberg uncertainty principle, the QBA puts a limitation-the so-called standard quantum limit-on the precision of sensing of position, velocity and acceleration. Here we show that QBA on a macroscopic mechanical oscillator can be evaded if the measurement of motion is conducted in the reference frame of an atomic spin oscillator. The collective quantum measurement on this hybrid system of two distant and disparate oscillators is performed with light. The mechanical oscillator is a vibrational 'drum' mode of a millimetre-sized dielectric membrane, and the spin oscillator is an atomic ensemble in a magnetic field. The spin oriented along the field corresponds to an energetically inverted spin population and realizes a negative-effective-mass oscillator, while the opposite orientation corresponds to an oscillator with positive effective mass. The QBA is suppressed by -1.8 decibels in the negative-mass setting and enhanced by 2.4 decibels in the positive-mass case. This hybrid quantum system paves the way to entanglement generation and distant quantum communication between mechanical and spin systems and to sensing of force, motion and gravity beyond the standard quantum limit.

Broadband quantum back action evading measurements of a resonant force

Quantum mechanics places a fundamental limit on the precision of continuous measurements. The Heisenberg uncertainty principle dictates that as the precision of a measurement of an observable (for example, position) increases, back action creates increased uncertainty in the conjugate variable (for example, momentum). In interferometric gravitational-wave detectors, higher laser powers reduce the position uncertainty created by shot noise(the photon-counting error caused by the quantum nature of the laser) but necessarily do so at the expense of back action in the form of quantum radiation pressure noise (QRPN)1. Once at design sensitivity, the gravitational-wave detectors Advanced LIGO2, VIRGO3 and KAGRA4 will be limited by QRPN at frequencies between 10hertz and 100hertz. There exist several proposals to improve the sensitivity of gravitational-wave detectors by mitigating QRPN5-10, but until now no platform has allowed for experimental tests of these ideas. Here we present a broadband measurement of QRPN at room temperature at frequencies relevant to gravitational-wave detectors. The noise spectrum obtained shows effects due to QRPN between about 2kilohertz and 100kilohertz, and the measured magnitude of QRPN agrees with our model. We now have a testbed for studying techniques with which to mitigate quantum back action, such as variational readout and squeezed light injection7, with the aim of improving the sensitivity of future gravitational-wave detectors.

Since the first communication systems were developed, the scientific community has been witnessing attempts to increase the amount of information that can be transmitted. In the last 10--15 years there has been a tremendous amount of research towards developing multi-antenna systems which would hopefully provide high-data-rate transmissions. However, increasing the overall amount of transmitted information increases the complexity of the necessary signal processing. A large portion of this thesis deals with several important issues in signal processing of multi-antenna systems. In almost every particular case the goal is to develop a technique/algorithm so that the overall complexity of the signal processing is significantly decreased. In the first part of the thesis a very important problem of signal detection in MIMO (multiple-input multiple-output) systems is considered. The problem is analyzed in two different scenarios: when the transmission medium (channel) 1) is known and 2) is unknown at the receiver. The former case is often called coherent and the later non-coherent MIMO detection. Both cases usually amount to solving highly complex NP-hard combinatorial optimization problems. For the coherent case we develop a significant improvement of the traditional sphere decoder algorithm commonly used for this type of detection. An interesting connection between the new improved algorithm and the H-infinity estimation theory is established, and the performance improvement over the standard sphere decoder is demonstrated. For the non-coherent case we develop a counterpart to the standard sphere decoder, the so-called out-sphere decoder. The complexity of the algorithm is viewed as a random variable; its expected value is analyzed and shown to be significantly smaller than the one of the overall exhaustive search. In the non-coherent case, in addition to the complexity analysis of the exact out-sphere decoder, we analyze the performance loss of a suboptimal technique. We show that only a moderate loss of a few dbs in power required at the transmitter will occur if a polynomial algorithm based on the semi-definite relaxation is used in place of any exact technique (which of course is not known to be polynomial). In the second part of the thesis we consider a few problems that arise in wireless broadcast channels. Namely, we consider the problem of the information symbol vector design at the transmitter. A polynomial linear precoding technique is constructed. It enables achieving data rates very close to the ones achieved with DPC (dirty paper coding) technique. Additionally, for another suboptimal polynomial scheme (the so-called nulling and cancelling), we show that it asymptotically achieves the same data rate as the optimal, exponentially complex, DPC. In the last part of the thesis we consider a quantum counterpart of the signal detection from classical communication. In quantum systems the signals are quantum states and the quantum detection problem amounts to designing measurement operators which have to satisfy certain quantum mechanics laws. A specific type of quantum detection called unambiguous detection, which has numerous applications including quantum filtering, has recently attracted a lot of attention in the research community. We develop a general framework for numerically solving this problem using the tools from the convex optimization theory. Furthermore, in the special case where the two quantum states are of rank 2, we construct an explicit analytical solution for the measurement operators. At the end we would like to emphasize that the contribution of this thesis goes beyond the specific problems mentioned here. Most algorithmic optimization techniques developed in this paper are generally applicable. While it is a fact that our results were originally motivated by wireless and quantum communications applications, we believe that the developed techniques will find applications in many different areas where similar optimization problems appear.

We apply the strategy of the back action evading measurement of a quadrature component of mechanical motion of a test mass to detection of a classical force acting on the mass (Science, 209, (1980) 547) and study both classical and quantum limitations of the technique. We are considering a resonant displacement transducer interrogated with a dichromatic optical pump as a model system in this study. The transducer is represented by a Fabry Perot cavity with a totally reflecting movable end mirror the resonant force of interest acts upon. The cavity is pumped with two coherent optical carriers equally detuned from one of the cavity resonances. We show that the quantum back action cannot be completely excluded from the measurement result due to the dynamic instability of the opto-mechanical system that either limits the allowable power of the optical pump or calls for introducing an asymmetry to the pump configuration destroying the quantum nondemolition nature of the measurement.

Quantum physics ultimately constrains how well sensors of position, speed and acceleration can perform. A hybrid quantum system that avoids these constraints could give rise to improved sensor technologies. See Letter p.191 The Heisenberg uncertainty principle imposes a fundamental limit on measurement precision and is intertwined with the effect of quantum back-action. This effect occurs when measuring the position of an object results in a small but certain random perturbation of its momentum. Eugene Polzik and colleagues demonstrate a way to evade quantum back-action by coupling the object under observation, a mechanical oscillator, to another oscillator. The mechanical oscillator is a millimetre-sized suspended membrane, which they couple to an ensemble of atomic spins. The trick is to measure the motion of the membrane in the reference frame of the atomic system, which is tuned to a regime of negative effective mass. This results in suppression of the quantum back-action on the membrane. This technique could be used for sensing force, motion and gravity beyond the limit imposed by the Heisenberg uncertainty principle.

Weakly measuring many-body systems and allowing for feedback in real time can simultaneously create and measure new phenomena in quantum systems. We theoretically study the dynamics of a continuously measured two-component Bose-Einstein condensate (BEC) potentially containing a domain wall and focus on the tradeoff between usable information obtained from measurement and quantum backaction. Each weakly measured system yields a measurement record from which we extract real-time dynamics of the domain wall. We show that quantum backaction due to measurement causes two primary effects: domain-wall diffusion and overall heating. The system dynamics and signal-to-noise ratio depend on the choice of measurement observable. We propose a feedback protocol to dynamically create a stable domain wall in the regime where domain walls are unstable, giving a prototype example of Hamiltonian engineering using measurement and feedback.

Second-generation interferometric gravitational-wave detectors will be operating at the Standard Quantum Limit (SQL), a sensitivity limitation set by the trade off between measurement accuracy and quantum back action, which is governed by the Heisenberg Uncertainty Principle. We review several schemes that allows the quantum noise of interferometers to surpass the SQL significantly over a broad frequency band. Such schemes may be an important component of the design of third-generation detectors.

The quantum radiation pressure and the quantum shot noise in laser-interferometric gravitational wave detectors constitute a macroscopic manifestation of the Heisenberg inequality. If quantum shot noise can be easily observed, the observation of quantum radiation pressure noise has been elusive, so far, due to the technical noise competing with quantum effects. Here, we discuss the evidence of quantum radiation pressure noise in the Advanced Virgo gravitational wave detector. In our experiment, we inject squeezed vacuum states of light into the interferometer in order to manipulate the quantum backaction on the 42kg mirrors and observe the corresponding quantum noise driven displacement at frequencies between 30 and 70Hz. The experimental data, obtained in various interferometer configurations, is tested against the Advanced Virgo detector quantum noise model which confirmed the measured magnitude of quantum radiation pressure noise.

It is known that the N=2 Wess–Zumino supersymmetric quantum mechanical model has p−1 degenerate zero-energy ground states consisting of only bosonic states, where p≥3 is the degree of the polynomial superpotential V(z)(z∈C) of the model [Jaffe et al. Ann. Phys. (NY) 178, 313 (1987)]. In this paper, the mathematical structure of the degenerate ground states is analyzed in the special case V(z)=λzp (λ>0). The following facts are discovered: (i) there exists a strongly continuous one parameter unitary group acting as a symmetry group in the quantum system under consideration; (ii) the generator of the symmetry group has infinitely many eigenspaces ℋm, m∈Z, and the bosonic part H+ of the Hamiltonian of the model is reduced by each of them; and (iii) there exist exactly p−1 ℋm’s in each of which the reduced part of H+ has a unique zero-energy ground state. It is noted also that H+ has infinitely many generalized eigenfunctions with eigenvalue zero. Moreover, a family of operators interrelating the zero-energy ground states is constructed. The coupling constant dependence of the nonzero eigenvalues of H+ is exactly found.

In this paper, we explore the quantum system of non-relativistic particles in a unique scenario: a circularly symmetric and static three-dimensional wormhole space-time accompanied by cosmic strings. We focus on a specific case where the redshift function varPhi (r) to be zero and defining the shape function as A(r)=frac{b}{r^2}. After establishing this background space-time, we investigate the behavior of a harmonic oscillator within the same wormhole context. By doing so, we observe the effects of the cosmic string and wormhole throat radius on the eigenvalue solution of the oscillator’s eigenvalue problem. The primary finding is that these cosmic features lead to modifications in the energy spectrum and wave functions of the system, breaking the degeneracy of energy levels that would typically be present in a more conventional setting. As a particular case, we present the specific energy level E_{1,ell } and the corresponding wave function psi _{1,ell }, which are associated with the ground state of the quantum system. These results highlight the fascinating and unique properties of the harmonic oscillator in the background of a circularly symmetric, static wormhole space-time with cosmic strings.

Reduced role of the wavefunctions' curvature of quantum potentials in non-standard quantum systems

We report an alternate formulation of the quantum master equation (QME) to describe the dynamics of a quantum system weakly coupled to a heat bath, in the presence of weak external driving. A key feature of this approach is the introduction of an explicit Hamiltonian to model the thermal fluctuations in the heat bath. We show that the resulting time coarse-grained dynamical equation for the quantum system has dissipators with a natural regulator, which emerges from an ensemble average over the fluctuations. Importantly, such regularized dissipators arise from the second-order contributions of both the external drive as well as the system-environment coupling. We show that the second-order drive terms, regularized to time-scales set by the fluctuations, result in dynamic drive-induced frequency shifts as well as drive-dependent relaxation phenomena. Considering the specific case of an ensemble of two-level systems, subjected to a linearly polarized external drive, we derive the modified Bloch Equations with such drive-dependent shift and damping terms. The resulting drive-induced frequency shifts converge to the known forms of dynamic frequency shifts, such as the Bloch-Siegert shift or the dynamic Stark shift, in appropriate limits. The Kramers-Kronig pairs of these frequency shifts - manifest as drive-dependent damping terms in the modified Bloch Equations and help explain the Redfield limit of free-induction-decay (FID) rates as well as the non-Bloch decay of Rabi oscillations in isotropic medium. Our method predicts correct orders of magnitudes of non-Bloch decay rates in isotropic medium as well as their observed temperature dependence. The QME reported here, correctly describes all known aspects of the driven-dissipative dynamics up to second-order of an open quantum system with appropriate thermal signatures and as such is expected to provide deeper insights into the study of quantum information processing on real systems.

Here we use approaches and concepts from quantum mechanics in order to analyze the propagation of classical electromagnetic waves in the elements of integrated optical circuits. These waveguide circuits are considered as potential wells between complex-shapes barriers formed by opaque media. This allowed us to construct in the framework of the slow-varying amplitude approximation for the wave equation an analogy between coherent oscillations in a quantum system and the redistribution in space of the field strength of a classical wave. We also demonstrated the methods to control the mode composition of a classical light in a spatially inhomogeneous waveguide structure. The proposed description was based on the analogy with Rabi-type oscillations in quantum mechanics.

Richard Feynman's observation that certain quantum mechanical effects cannot be simulated efficiently on a computer led to speculation that computation in general could be done more efficiently if it used these quantum effects. This speculation proved justified when Peter Shor described a polynomial time quantum algorithm for factoring intergers. In quantum systems, the computational space increases exponentially with the size of the system, which enables exponential parallelism. This parallelism could lead to exponentially faster quantum algorithms than possible classically. The catch is that accessing the results, which requires measurement, proves tricky and requires new nontraditional programming techniques. The aim of this paper is to guide computer scientists through the barriers that separate quantum computing from conventional computing. We introduce basic principles of quantum mechanics to explain where the power of quantum computers comes from and why it is difficult to harness. We describe quantum cryptography, teleportation, and dense coding. Various approaches to exploiting the power of quantum parallelism are explained. We conclude with a discussion of quantum error correction.