Recent developments in quantum computing suggest that it could be possible to make conditional changes to the state of a quantum mechanical system without resorting to classical observation. It is accomplished through collective response of atoms comprising a lattice for the system and involves relative phase adjustments only. We exploit this possibility and describe experimental designs that could help elucidate quantum mechanical properties of these systems and distinguish between interpretations.
We apply the Frobenius (power-series) method to some simple exactly-solvable and conditionally-solvable quantum-mechanical models with supposed physical interest. We show that the supposedly exact solutions to radial eigenvalue equations derived in recent papers are not correct because they do not satisfy some well-known theorems. We also discuss the origin of the mistake by means of the approach indicated above.
We analyze two conditionally solvable quantum-mechanical models: a one-dimensional sextic oscillator and a perturbed Coulomb problem. Both lead to a three-term recurrence relation for the expansion coefficients. We show diagrams of the distribution of their exact eigenvalues with the addition of accurate ones from variational calculations. We discuss the symmetry of such distributions. We also comment on the wrong interpretation of the exact eigenvalues and eigenfunctions by some researchers that has led to the prediction of allowed cyclotron frequencies and field intensities.
Backaction-evading measurements of mechanical motion can achieve precision below the zero-point uncertainty and quantum squeezing, which makes them a resource for quantum metrology and quantum information processing. We provide an exact expression for the conditional state of an optomechanical system in a two-tone backaction-evading measurement beyond the standard adiabatic approximation and perform extensive numerical simulations to go beyond the usual rotating-wave approximation. We predict the simultaneous presence of conditional mechanical squeezing, intra-cavity squeezing, and optomechani…
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical representation of classical conditional probabilities is situated within the broader frame of noncommutative representations. To this goal, we adopt some parts of the quantum formalism and ask whether empirical data can constrain the rest of the representation to conform to quantum mechanics. We will show that as the set of empirical data grows conventional el…
We study single photon optomechanics conditioned on photon counting events. By selecting only detection events that occur long after a photon pulse arrives at the cavity, the optomechanical interaction time can be increased, allowing a large momentum kick to be applied to the oscillator. We apply this to two optomechanical cavities set up within a Mach-Zhender interferometer driven by a single photon source. The conditional state of the mechanical modes in such a system becomes an entangled cat state for detection times resulting in maximum mechanical amplitude in phase space. Further we study…
A mechanical system can be optimally controlled through continuous measurements of its position followed by feedback. We revisit the complete formalism for predicting the performance of such as system without invoking the standard rotating wave approximations and the adiabatic approximation. Using this formalism we deduce both the conditional and unconditional state of a mechanical oscillator using the optimal control and feedback that leads to mechanical cooling and mechanical squeezing. We find large discrepancies between the exact solutions and the approximate solutions stressing the import…
The quantum mechanical no-cloning theorem for pure states is generalized and transfered to the quantum logics with a conditional probability calculus in a rather abstract, though simple and basic fashion without relying on a tensor product construction or finite dimension as required in other generalizations.
Standard Quantum Limit (SQL) of a classical mechanical force detection results from quantum back action impinged by the meter on a probe mechanical transducer perturbed by the force of interest. In this paper we introduce a technique of continuous \vy{broadband} back action avoiding measurements for the case of a resonant signal force acting on a linear mechanical oscillator supporting one of mirrors of an optical Michelson-Sagnac Interferometer (MSI). The interferometer with the movable mirror is an opto-mechanical transducer able to support polychromatic probe field. The method involves a di…
We consider the dynamical behavior of a nanomechanical mirror in a high-quality cavity under the action of a coupling laser and a probe laser. We demonstrate the existence of the analog of electromagnetically induced transparency (EIT) in the output field at the probe frequency. Our calculations show explicitly the origin of EIT-like dips as well as the characteristic changes in dispersion from anomalous to normal in the range where EIT dips occur. Remarkably the pump-probe response for the opto mechanical system shares all the features of the Lambda system as discovered by Harris and collabor…
A new quantum mechanical notion -- Conditional Density Matrix -- is discussed and is applied to describe some physical processes. This notion is a natural generalization of von Neumann density matrix for such processes as divisions of quantum systems into subsystems and reunifications of subsystems into new joint systems. Conditional Density Matrix assigns a quantum state to a subsystem of a composite system under condition that another part of the composite system is in some pure state.
We theoretically study the transparency and amplification of a weak probe field applied to the cavity in hy- brid systems formed by a driven superconducting circuit QED system and a mechanical resonator, or a driven optomechanical system and a superconducting qubit. We find that both the mechanical resonator and the su- perconducting qubit can result in the transparency to a weak probe field in such hybrid systems when a strong driving field is applied to the cavity. We also find that the weak probe field can be amplified in some parameter regimes. We further study the statistical properties o…
A novel regime of atom-cavity physics is explored, arising when large atom samples dispersively interact with high-finesse optical cavities. A stable far detuned optical lattice of several million rubidium atoms is formed inside an optical ring resonator by coupling equal amounts of laser light to each propagation direction of a longitudinal cavity mode. An adjacent longitudinal mode, detunedby about 3 GHz, is used to perform probe transmission spectroscopy of the system. The atom-cavity coupling for the lattice beams and the probe is dispersive and dissipation results only from the finite pho…
We propose a scheme that can generate a tunable double optomechanically induced transparency (OMIT) in a hybrid optomechanical cavity system, in which the mechanical resonator of an optomechanical cavity is coupled to an additional mechanical resonator, and the additional mechanical resonator can be driven by a weak external coherently mechanical driving field. We show that both the intensity and the phase of the the external mechanical driving field can control the propagation of the probe field, including changing the transmission spectrum curve from a double-window to a single-window. Our s…
We study the directional amplification of an optical probe field in a three-mode optomechanical system, where the mechanical resonator interacts with two linearly-coupled optical cavities and the cavities are driven by strong optical pump fields. The optical probe field is injected into one of the cavity modes, and at the same time, the mechanical resonator is subject to a mechanical drive with the driving frequency equal to the frequency difference between the optical probe and pump fields. We show that the transmission of the probe field can be amplified in one direction and de-amplified in …
The probability `measure' for measurements at two consecutive moments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We demonstrate that there are only two ways to resolve this problem. The first solution places emphasis on the precise use of the concept of conditional probability for successive measurements. The physically correct conditional probabilities define additive probabilities for two-time measurements. These probabilities depend explicitly on the resolution of the…
We propose measurement based conditional generation of superposition of motional states of nanomechanical resonator. We consider a two level quantum mechanical system coupled with nanomechanical resonator through phonon exchange. An interaction, which produces shifts in the state of nanomechanical resonator depending on the state of the qubit, is realized by driving qubit through two resonant lasers. The measurement of the state of quantum mechanical system produces superposition states of nanomechanical resonator. We show that the quantum interference between states in superposition may lead …
Entanglement is one of the most intriguing aspects of quantum mechanics and lies at the heart of the ongoing Second Quantum Revolution, where it is a resource that is used in quantum key distribution, quantum computing and quantum teleportation. We report experiments demonstrating the crucial role that entanglement plays in pump-probe experiments involving ionization, which are a hallmark of the novel research field of attosecond science. We demonstrate that the degree of entanglement in a bipartite ion plus photoelectron system, and, as a consequence, the degree of vibrational coherence in th…
We investigate the properties of the optical output fields from a cavity optomechanical system, where the cavity is driven by a strong coupling and a weak probe optical fields and the mechanical resonator is driven by a coherent mechanical pump. When the frequency of the mechanical pump matches the frequency difference between the coupling and probe optical fields, due to the interference between the different optical components at the same frequency, we demonstrate that the large positive or negative group delay of the output field at the frequency of probe field can be achieved and tuned by …
Conditional expectation values of quantum mechanical observables reflect unique non-classical correlations, and are generally sensitive to decoherence. We consider the circumstances under which such sensitivity to decoherence is removed, namely, when the measurement process is subjected to conservation laws. Specifically, we address systems with additive conserved quantities and identify sufficient conditions for the system state such that its coherence plays no role in the conditional expectation values of observables that commute with the conserved quantity. We discuss our findings for a spe…
We propose a scheme to probe quantum coherence in the state of a nano-cantilever based on its magnetic coupling (mediated by a magnetic tip) with a spinor Bose Einstein condensate (BEC). By mapping the BEC into a rotor, its coupling with the cantilever results in a gyroscopic motion whose properties depend on the state of the cantilever: the dynamics of one of the components of the rotor angular momentum turns out to be strictly related to the presence of quantum coherence in the state of the cantilever. We also suggest a detection scheme relying on Faraday rotation, which produces only a very…
Graphical models of probabilistic dependencies have been extensively investigated in the context of classical uncertainty. However, in some domains (most notably, in computational physics and quantum computing) the nature of the relevant uncertainty is non-classical, and the laws of classical probability theory are superseded by those of quantum mechanics. In this paper we introduce Markovian Entanglement Networks (MEN), a novel class of graphical representations of quantum-mechanical dependencies in the context of such non-classical systems. MEN are the quantum-mechanical analogue of Markovia…
We address the macroscopic quantumness of the state of mechanical systems subjected to conditional protocols devised for state engineering in cavity optomechanics. We use a measure of macroscopicity based on phase-space methods. We cover the domain from weak to strong optomechanical coupling, illustrating how measurements performed over the cavity field that drives the dynamics of a mechanical system are able to steer the latter towards large quantum coherent states. The effect of losses is evaluated for the case of an open cavity, and analyzed in terms of the features of the Wigner functions …
Many theories of quantum gravity can be understood as imposing a minimum length scale the signatures of which can potentially be seen in precise table top experiments. In this work we inspect the capacity for correlated many body systems to probe non-classicalities of spacetime through modifications of the commutation relations. We find an analytic derivation of the dynamics for a single mode light field interacting with a single mechanical oscillator and with coupled oscillators to first order corrections to the commutation relations. Our solution is valid for any coupling function as we work…
We study the propagation of a weak probe field through an optomechanical system in which $N$ nearly degenerate mechanical membranes are inside a Febry-Perot cavity, and couple dispersively to an intracavity field. We derive a general analytical expression for the output probe field. We show that the in-phase quadrature of the output probe field can exhibit multiple electromagnetically induced transparency with at most $N$ narrow transparency windows. We find that the superluminal light can be achieved with at most $N$ different negative group velocities at the transparency windows. Moreover, b…
Nanomechanical resonators (NMRs), as the quantum mechanical sensing probers, have played the important roles for various high-precision quantum measurements. Differing from the previous emission spectral probes (i.e., the NMR modified the atomic emission), in this paper we propose an alternative approach, i.e., by probing the scattering spectra of the quantum mechanical prober coupled to the driving microwaves, to characterize the physical features of the NMR embedded in a rf-SQUID based superconducting qubit. It is shown that, from the observed specifical frequency points in the spectra, i.e.…
Laser cooling is a fundamental technique used in primary atomic frequency standards, quantum computers, quantum condensed matter physics and tests of fundamental physics, among other areas. It has been known since the early 1990s that laser cooling can, in principle, be improved by using squeezed light as an electromagnetic reservoir; while quantum feedback control using a squeezed light probe is also predicted to allow improved cooling. Here, we implement quantum feedback control of a micro-mechanical oscillator for the first time with a squeezed probe field. This allows quantum-enhanced feed…
We describe an optomechanical system in which the mean phonon number of a single mechanical mode conditionally displaces the amplitude of the optical field. Using homodyne detection of the output field we establish the conditions under which phonon number quantum jumps can be inferred from the measurement record: both the cavity damping rate and the measurement rate of the phonon number must be much greater than the thermalization rate of the mechanical mode. We present simulations of the conditional dynamics of the measured system using the stochastic master equation. In the good-measurement …
We report on a hitherto unexplored application of squeezed light: for quantum-enhancement of mechanical transduction sensitivity in microcavity optomechanics. Using a toroidal silica microcavity, we experimentally demonstrate measurement of the transduced phase modulation signal with a sensitivity $-0.72(\pm 0.01)$\,dB below the shot noise level. This is achieved for resonant probing in the highly under-coupled regime, by preparing the probe in a weak coherent state with phase squeezed vacuum states at sideband frequencies.
We theoretically investigate the coupling of an ultracold three-level atomic gas and a nano-mechanical mirror via classical electromagnetic radiation. The radiation pressure on the mirror is modulated by absorption of a probe light field, caused by the atoms which are electromagnetically rendered nearly transparent, allowing the gas to affect the mirror. In turn, the mirror can affect the gas as its vibrations generate opto-mechanical sidebands in the control field. We show that the sidebands cause modulations of the probe intensity at the mirror frequency, which can be enhanced near atomic re…
The development of useful photon-photon interactions can trigger numerous breakthroughs in quantum information science, however this has remained a considerable challenge spanning several decades. Here we demonstrate the first room-temperature implementation of large phase shifts ($\approxπ$) on a single-photon level probe pulse (1.5us) triggered by a simultaneously-propagating few-photon-level signal field. This process is mediated by $Rb^{87}$ vapor in a double-$Λ$ atomic configuration. We use homodyne tomography to obtain the quadrature statistics of the phase-shifted quantum fields and per…
Pulsed optomechanical measurements enable squeezing, non-classical state creation and backaction-free sensing. We demonstrate pulsed measurement of a cryogenic nanomechanical resonator with record precision close to the quantum regime. We use these to prepare thermally squeezed and purified conditional mechanical states, and to perform full state tomography. These demonstrations exploit large photon-phonon coupling in a nanophotonic cavity to reach a single-pulse imprecision of 9 times the mechanical zero-point amplitude $x_\mathrm{zpf}$. We study the effect of other mechanical modes which lim…
In a recent letter [Phy. Rev. Lett. 95, 080502 (2005)], it is claimed that based on a new kind of quantum mechanical phase of wave function which is neither dynamical nor geometrical a new kind of phase gate for quantum computation is discovered. The origin of this phase is the adiabatic evolution of a dark state. I would like to point out that these claims are questionable. The so called new phase gate was based on a phase which was nothing new but has been known for decades. It is something which has no physical meaning and is not observable. It was also pointed out by [quant-ph/0509150v1] t…
We discuss the problem of estimating a frequency via N-qubit probes undergoing independent dephasing channels that can be continuously monitored via homodyne or photo-detection. We derive the corresponding analytical solutions for the conditional states, for generic initial states and for arbitrary efficiency of the continuous monitoring. For the detection strategies considered, we show that: i) in the case of perfect continuous detection, the quantum Fisher information (QFI) of the conditional states is equal to the one obtained in the noiseless dynamics; ii) for smaller detection efficiencie…
Optomechanical systems are promising platforms for controlled light-matter interactions. They are capable of providing several fundamental and practical novel features when the mechanical oscillator is cooled down to nearly reach its ground state. In this framework, measuring the effective temperature of the oscillator is perhaps the most relevant step in the characterization of those systems. In conventional schemes, the cavity is driven strongly, and the overall system is well-described by a linear (Gaussian preserving) Hamiltonian. Here, we depart from this regime by considering an undriven…
Interfacing between matter qubits and light is a crucial provision for numerous quantum technological applications. However, a generic qubit may not directly interact with a relevant optical field mode, and hence, one could necessitate to adjust frequencies to match resonance conditions between parties. In this work, we show how a parametric coupling of the qubit with a mechanical oscillator, in conjunction with the trilinear radiation pressure coupling of the same object with light, can induce maximal qubit-light entanglement at an optimal time. We also show how our method enables conditional…
We show that the interaction of a pulsed laser light with a mechanical oscillator through the radiation pressure results in an opto-mechanical entangled state in which the photon number is correlated with the oscillator position. Interestingly, the mechanical oscillator can be delocalized over a large range of positions when driven by an intense laser light. This provides a simple yet sensitive method to probe hypothetic post-quantum theories including an explicit wave function collapse model, like the Diosi and Penrose model. We propose an entanglement witness to reveal the quantum nature of …
We propose a spectroscopic approach to probe tiny vibrations of a nanomechanical resonator (NAMR), which may reveal classical or quantum behavior depending on the decoherence-inducing environment. Our proposal is based on the detection of the voltage-fluctuation spectrum in a superconducting transmission line resonator (TLR), which is {\it indirectly} coupled to the NAMR via a controllable Josephson qubit acting as a quantum transducer. The classical (quantum mechanical) vibrations of the NAMR induce symmetric (asymmetric) Stark shifts of the qubit levels, which can be measured by the voltage …
We present a mathematical framework for quantum mechanics in which the basic entities and operations have physical significance. In this framework the primitive concepts are states and effects and the resulting mathematical structure is a convex effect algebra. We characterize the convex effect algebras that are classical and those that are quantum mechanical. The quantum mechanical ones are those that can be represented on a complex Hilbert space. We next introduce the sequential product of effects to form a convex sequential effect algebra. This product makes it possible to study conditional…
We propose a novel scheme to realize electrically controlled quantum memories in the opto- and electro-mechanical (OEM) cavity. Combining this OEM cavity with the mechanism of Electromagnetically Induced Transparency (EIT) we find that the quantum interference, arising from the two optical transitions of the $Λ$ type three-level atomic ensembles, can be manipulated electrically. Numerical calculations show that the probe photon state can be well stored into the atomic spin state by sending an electric current pulse and retrieved with time-reverse symmetry by sending the other current pulse wit…
We present optical sideband spectroscopy measurements of a mesoscopic mechanical oscillator cooled near its quantum ground state. The mechanical oscillator, corresponding to a 3.99GHz acoustic mode of a patterned silicon nanobeam, is coupled via radiation pressure to a pair of co-localized 200THz optical modes. The mechanical mode is cooled close to its quantum ground state from a bath temperature of 18K using radiation pressure back-action stemming from the optical pumping of one of the optical cavity resonances. An optical probe beam, resonant with the second optical cavity resonance, is use…
Some authors have raised the question whether the probabilities stemming from a quantum mechanical computation are entitled to enter the Bell and the Clauser-Horne inequalities. They have remarked that if the quantum probabilities are given the status of conditional ones and the statistics for the various settings of the detectors in a given experiment is properly kept into account, the inequalities happen to be no longer violated. In the present paper a classical simile modeled after the quantum mechanical instances is closely scrutinised. It is shown that the neglect of the conditional chara…
We explore theoretically the optical response properties in an optomechanical system under electromagneti- cally induced transparency condition but with the mechanical resonator being driven by an additional coherent field. In this configuration, more complex quantum coherent and interference phenomena occur. In partic- ular, we find that the probe transmission spectra depend on the total phase of the applied fields. Our study also provides an efficient way to control propagation of amplification.
We study the quantum measurement of a cantilever using a parametrically-coupled electromagnetic cavity which is driven at the two sidebands corresponding to the mechanical motion. This scheme, originally due to Braginsky et al. [V. Braginsky, Y. I. Vorontsov, and K. P. Thorne, Science 209, 547 (1980)], allows a back-action free measurement of one quadrature of the cantilever's motion, and hence the possibility of generating a squeezed state. We present a complete quantum theory of this system, and derive simple conditions on when the quantum limit on the added noise can be surpassed. We also s…
In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate--the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a "typical" choice in the macrostate (the Statistical Postulate). Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there are two sources of randomness in…
Hardware-Agnostic Modeling of Quantum Side-Channel Leakage via Conditional Dynamics and Learning from Full Correlation Data
Know Center GmbH（Know Center有限公司）；University of Graz（格拉茨大学）；Stevens Institute of Technology（史蒂文斯理工学院）；Technische Universität Wien（维也纳工业大学）；IQOQI Vienna, Austrian Academy of Sciences（奥地利科学院维也纳量子光学与量子信息研究所）
Can quantum-mechanical particles propagating on a fixed spacetime background be approximated as test bodies satisfying the weak equivalence principle? We ultimately answer the question in the negative but find that, when universality of free-fall is assessed locally, a nontrivial agreement between quantum mechanics and the weak equivalence principle exists. Implications for mass sensing by quantum probes are discussed in some details.
Quantum electro-mechanical systems offer a unique opportunity to probe quantum noise properties in macroscopic devices, properties which ultimately stem from the Heisenberg Uncertainty Principle. A simple example of this is expected to occur in a microwave parametric transducer, where mechanical motion generates motional sidebands corresponding to the up and down frequency-conversion of microwave photons. Due to quantum vacuum noise, the rates of these processes are expected to be unequal. We measure this fundamental imbalance in a microwave transducer coupled to a radio-frequency mechanical m…
