NOON States Research Articles

Atoms versus photons as carriers of quantum states

The problem of the complete transfer of quantum states and entanglement in a four-qubit system composed of two single-mode cavities and two two-level atoms is investigated. The transfer of single and double excitation states is discussed for two different coupling configurations between the qubits. In the first, the coupling is mediated by the atoms that simultaneously couple to the cavity modes. In the second configuration, each atom resides inside one of the cavities and the coupling between the cavities is mediated by the overlapping field modes. A proper choice of basis states makes it possible to identify states that could be completely transferred between themselves. Simple expressions are derived for the conditions for the complete transfer of quantum states and entanglement. These conditions impose severe constraints on the evolution of the system in the form of constants of motion. The constrains on the evolution of the system imply that not all states can evolve in time, and we find that the evolution of the entire system can be confined into that occurring among two states only. Detailed analysis show that in the case where the interaction is mediated by the atoms, only symmetric superposition states can be completely and reversibly transferred between the atoms and the cavity modes. In the case where the interaction is mediated by the overlapping field modes, both symmetric and antisymmetric superposition states can be completely transferred. We also show that the system is capable of generating purely photonic NOON states, but only if the coupling is mediated by the atoms, and demonstrate that the ability to generate the NOON states relies on perfect transfer of an entanglement from the atoms to the cavity modes.

Generation of W state and NOON state of distant polar molecules ensembles via a triple hybrid device

A scheme is proposed to generate the W state and NOON state for the collective molecular modes of distant polar molecules ensembles via a triple hybrid device. Through the virtual excitation of the microwave photons of the transmission-line resonators, the interaction between the superconducting charge qubit and the polar molecules induces the entanglement for the collective modes of the polar molecules. The enhanced effective coupling strength between the superconducting charge qubit and the polar molecules enables to generate the W state and NOON state with high fidelity.

Generation of NOON states via Raman transitions in a bimodal cavity

We propose a scheme for generation of NOON states via Raman transitions. In the scheme, a double $$\varLambda $$ -type three-level atom is trapped in a high-Q bimodal cavity which is initially in vacuum states. After a series of operations and suitable interaction time, we can obtain highly nonclassical entangled states of one atom and N photons. Then it can easily be converted to purely photonic NOON states by application of a single projective measurement on the atom. The successful probability and fidelity of the scheme are finally discussed.

Quantum reading of digital memory with non-Gaussian entangled light

It has been shown recently S. Pirandola [Phys. Rev. Lett. 106, 090504 (2011)] that entangled light with Einstein-Podolsky-Rosen correlations retrieves information from digital memory better than any classical light. In identifying this, a model of digital memory with each cell consisting of a reflecting medium with two reflectivities (each memory cell encoding the binary numbers 0 or 1) is employed. The readout of binary memory essentially corresponds to discrimination of two bosonic attenuator channels characterized by different reflectivities. The model requires an entire mathematical paraphernalia of a continuous variable Gaussian setting for its analysis when arbitrary values of reflectivities $0\ensuremath{\le}{r}_{0},{r}_{1}\ensuremath{\le}1$ are considered. Here we restrict ourselves to a basic quantum readout mechanism with two different families of non-Gaussian entangled states of light, in which the binary channels to be discriminated are (i) ideal memory characterized by reflectivity ${r}_{1}=1$ (identity channel) and (ii) a thermal noise channel---where the signal light illuminating the memory location gets completely lost (${r}_{0}=0$) and only a white thermal noise hitting the upper side of the memory reaches the decoder. We compare the quantum reading efficiency of two families of non-Gaussian entangled light [($m,{m}^{\ensuremath{'}}$) family of path-entangled photon states and entangled state obtained by mixing a single photon with coherent light in a 50:50 beam splitter] with any classical source of light in this model. We identify that the classes of non-Gaussian entangled transmitters studied here offer significantly better reading performance than any classical transmitters of light in the regime of low signal intensity. We also demonstrate that the ($m,{m}^{\ensuremath{'}}$) family of entangled light exhibits better reading performance than NOON states.

Effect of interparticle interaction in a free-oscillation atomic interferometer

We investigate the dynamics of two interacting bosons repeatedly scattering off a beam-splitter in a free oscillation atom interferometer. Using the inter-particle scattering length and the beam splitter probabilites as our control parameters, we show that even in a simple setup like this a wide range of strongly correlated quantum states can be created. This in particular includes the NOON state, which maximizes the quantum Fisher information and is a foremost state in quantum metrology.

Generation of arbitrary symmetric entangled states with conditional linear optical coupling

An approach for generating the entangled photonic states |F1,F2>+|F2,F1> from two arbitrary states |F1> and |F2> is proposed. The protocol is implemented by the conditionally induced beam-splitter coupling which leads to the selective swapping between two photonic modes. Such coupling occurs in a quantum system prepared in the superposition of two ground states with only one of them being involved in the swapping. All the entangled states in the category, such as entangled pairs of coherent states or Fock states (N00N states), can be efficiently produced in the same way by this method.

Single-photon transport and mechanical NOON-state generation in microcavity optomechanics

We investigate the single-photon transport in a single-mode optical fiber coupled to an optomechanical system in the single-photon strong-coupling regime. The single-photon transmission amplitude is analytically obtained with a real-space approach and the effects of cavity and mechanical dissipations are studied via master-equation simulations. Based on the theoretical framework, we further propose a heralded probabilistic scheme to generate mechanical NOON states with arbitrary phonon numbers by measuring the sideband photons. The efficiency and fidelity of the scheme are discussed finally.

Creation of arbitrary Dicke and NOON states of trapped-ion qubits by global addressing with composite pulses

We propose a fast and efficient technique to create classes of highly entangled states of trapped ions, such as arbitrary Dicke states and superpositions of them, e.g. NOON states. The ions are initialized in the phonon ground state and are addressed globally with a composite pulse that is resonant with the first motional sideband. The technique is fairly robust to parameter fluctuations and operates on comparatively short time scales, as resonant interactions allow one to use the minimum laser pulse area. The number of single pulses from the composite sequence is equal to the number of ions; thus the implementation complexity grows only linearly with the size of the system. The approach does not require individual addressing of the ions in the trap and can be applied both inside and outside the Lamb–Dicke regime.

Enhancing entangled-state phase estimation by combining classical and quantum protocols

Here we describe a laboratory procedure by which we have increased the resolution of a measurement of the position of an optical component by a factor of 16. The factor of 16 arises from a four-fold quantum enhancement through the use of an N = 4 N00N state and a four-fold classical enhancement from a quadruple pass through a prism pair. The possibility of achieving supersensitivity using this method is discussed.

Wigner function of N00N state and quantum interference with N00N state as input

Using the formula of Wigner function in coherent representation, we have obtained the analytical expression for Wigner function of N00N state. Based on phase space method, we study the quantum interference with N00N state as input. We derive the analytical expression of conditional probability related with the input parameter N and phase parameter φ and analyze it numerically. It is shown that, when φ is 0 or π, the output is just N00N state. It is also shown that, for 2002 state as input, the output must be 2002 state, which is independent of phase parameters. Moreover, as the number of input photon N increases, the phase probability distributions remain to have one, two, three and four peaks and get narrower. All these results can offer theoretical reference for experiments.

Generation of MOON states in ion-laser interactions

A new class of entangled states, similar to N00N states is introduced. We call these states M00N states as the excitations shared in both subsystems do not need to be equal. The generation proposed here does not need conditional measurements, and therefore is achieved in a deterministic manner.

Unbounded quantum Fisher information in two-path interferometry with finite photon number

The minimum error of unbiased parameter estimation is quantified by the quantum Fisher information in accordance to the Cramér–Rao bound. We indicate that only superposed NOON states by simultaneous measurements can achieve the maximum quantum Fisher information with form for a given photon number distribution by a POVM in linear two-path interferometer phase measurement. We present a series of specified superposed states with infinite quantum Fisher information but with finite average photon numbers. The advantage of this unbounded quantum Fisher information will be beneficial to many applications in quantum technology.

Entanglement-enhanced probing of a delicate material system

Quantum metrology1 uses entanglement2,3,4,5 and other quantum effects6 to improve the sensitivity of demanding measurements7,8,9. Probing of delicate systems demands high sensitivity from limited probe energy and has motivated the field's key benchmark—the standard quantum limit10. Here we report the first entanglement-enhanced measurement of a delicate material system. We non-destructively probe an atomic spin ensemble by means of near-resonant Faraday rotation, a measurement that is limited by probe-induced scattering in quantum-memory and spin-squeezing applications6,11,12,13. We use narrowband, atom-resonant NOON states to beat the standard quantum limit of sensitivity by more than five standard deviations, both on a per-photon and per-damage basis. This demonstrates quantum enhancement with fully realistic loss and noise, including variable-loss effects14,15,16. The experiment opens the way to ultra-gentle probing of single atoms17, single molecules18, quantum gases19 and living cells20.

All-Resonant Control of Superconducting Resonators

An all-resonant method is proposed to control the quantum state of superconducting resonators. This approach uses a tunable artificial atom linearly coupled to resonators, and allows for efficient routes to Fock state synthesis, qudit logic operations, and synthesis of NOON states. This resonant approach is theoretically analyzed, and found to perform significantly better than existing proposals using the same technology.

Quantum metrology for nonlinear phase shifts with entangled coherent states

We investigate the phase enhancement of quantum states subject to non-linear phase shifts. The optimal phase estimation of even entangled coherent states (ECSs) is shown to be better than that of NOON states and of odd ECS states with the same average particle number <n> and non-linearity exponent k. We investigate the creation of approximate ECSs (AECSs) from a squeezed vacuum with current optical technology methods and find that a pure AECS is even slightly better than an even ECS for large <n>. We also examine simple but physically relevant cases of loss in the non-linear interferometer arm, for a fixed <n>.

Quantum metrology with entangled spin-coherent states of two modes

Recently, Gerry et al. [Phys. Rev. A 79, 022111 (2009)] studied the violation of the Bell-Clauser-Horne-Shimony-Holt inequality for two-spin systems, prepared in an entanglement of spin-coherent states, the so-called entangled spin-coherent states (ESCSs), and found maximal violations for a large class of states. In this paper, using the Holstein-Primakoff realization (HPR) of angular momentum algebra, we present an improved phase estimation scheme employing ESCSs and demonstrate that increasing the spin number gives the smallest variance in the phase parameter in comparison to NOON states under perfect and lossy conditions. The phase sensitivity of this interferometric scheme with parity detection on one of the output states is discussed.

Phase estimation by photon counting measurements in the output of a linear Mach–Zehnder interferometer

Photon counting measurements are analyzed for obtaining a classical phase parameter in linear Mach Zehnder interferometer (MZI), by the use of phase estimation theories. The detailed analysis is made for four cases: a) Coherent states inserted into the interferometer. b) Fock number state inserted in one input port of the interferometer and the vacuum into the other input port. c) Coherent state inserted into one input port of the interferometer and squeezed-vacuum state in the other input port. d) Exchanging the first beam-splitter (BS1) of a MZI by a non-linear system which inserts a NOON state into the interferometer and by using photon counting for parity measurements. The properties of photon counting for obtaining minimal phase uncertainties for the above special cases and for the general case are discussed.

Sub-Rayleigh Lithography Using High Flux Loss-Resistant Entangled States of Light

Quantum lithography achieves phase superresolution using fragile, experimentally challenging entangled states of light. We propose a scalable scheme for creating features narrower than classically achievable with reduced use of quantum resources and, consequently, enhanced resistance to loss. The scheme is an implementation of interferometric lithography using a mixture of a spontaneous parametric down-converted entangled state with intense classical coherent light. We measure coincidences of up to four photons mimicking multiphoton absorption. The results show a narrowing of the interference fringes of up to 30% with respect to the best analogous classical scheme using only 10% of the nonclassical light required for creating NOON states.

Efficient entanglement concentration for arbitrary less-entangled NOON states

We put forward an efficient entanglement concentration protocol (ECP) for arbitrary less-entangled NOON state. In the protocol, we resort to the weak cross-Kerr nonlinearity to complete this task. Different from other ECPs, this protocol can be reused to get a high success probability. We do not need to know the exact coefficients of the initial state. Moreover, we even do not need to know the exact photon number of the initial NOON state. This protocol may be useful and convenient in the current quantum information processing.

Multiphoton path-entanglement generation by concurrent parametric down-conversion in a singleχ(2)nonlinear photonic crystal

We propose a two-dimensional ${\ensuremath{\chi}}^{(2)}$ nonlinear photonic crystal capable of satisfying quasi-phase-matching conditions for two or three parametric down-conversions simultaneously. Seeded by a two-mode coherent state, this crystal can produce two-, three-, four-, or five-photon path-entangled states, provided the corresponding number photons are produced, i.e., in a postselection-free way. In particular, up to five-photon NOON state can be generated, which enables phase supersensitive measurements at the Heisenberg limit. The concurrent multiple quasi-phase-matchings provided by the nonlinear photonic crystal open up a way to integrated quantum light sources.