Squeezing Operator Research Articles

Coherently stimulated parametric down-conversion, phase effects, and quantum-optical interferometry

We re-examine the properties of the states produced by nondegenerate coherently stimulated parametric down-conversion wherein the signal and idler modes are seeded with coherent states of light and where the nonlinear crystal is driven by a strong classical field as described by the parametric approximation. The states produced are the two-mode squeezed coherent states defined with a specific ordering of operators, namely, the displacement operators of the two modes acting on the double vacuum state followed by the action of the two-mode squeeze operator representing the down-conversion process. Though mathematically equivalent to the reverse ordering of operators, but with different displacement parameters, the ordering we consider is closely related to what could most easily be implemented in the laboratory. The statistical properties of the state are studied with an emphasis on how they, and its average photon number, are affected by the various controllable phases, namely, those of the classical pump field of the two input coherent states. We then consider the multiphoton interference effects that arise if the two beams are overlapped on a 50:50 beam splitter, investigating the role of the phases in controlling the statistical properties of the output states. Finally, we study the prospects for the application of the states to quantum-optical interferometry to obtain sensitivities in phase-shift measurements beyond the standard quantum limit.

Quantum Properties of Single-Mode Squeezing and Two-Mode Squeezing Repeated Role Two-Mode Vacuum State

One new quantum state called single-mode squeezing and two-mode squeezing repeated role two-mode vacuum state (SMSTMSVT) is constructed by single-mode squeezing operator and two-mode squeezing operator repeated role in two-mode vacuum state. Its squeezing, antibunching effect, violation of Cauchy-Schwartze inequality and entanglement property between two modes are analyzed by the technique of integration with in an ordered product of operators. Unitary transformation of single-mode squeezing and that of two-mode squeezing are utilized in the calculation process. The influences of single-mode squeezing parameter on quantum properties are discussed. The results by numerical calculation show that its squeezing is strengthened with increasing of single-mode squeezing parameter, but its entanglement property and violation of Cauchy-Schwartze inequality are weakened with increasing of single-mode squeezing parameter. On the other hand, its antibunching effect is not influenced by single-mode squeezing parameter, and it always displays bunching effect.

Squeezing of arbitrary order: the ups and downs

We show how using classical von Neumann index theory makes possible a universal treatment of squeezing of arbitrary order. ‘Universal’ means that the same approach applied to displacement (order 1) and squeeze (order 2) operators confirms firmly and unequivocally what is already known as well as provides rigorous arguments that the higher order squeezing cannot be generalized in a ‘naive’ way. We create an environment for answering definitely all the emerging questions in positive ( the ups ) and negative ( downs ). In the latter case, we suggest ways for further development.

Wave functions of a new kind of nonlinear single-mode squeezed state

We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear single-mode squeezing operators. We derive the wave functions of exp[−(ig/2)(P + P)|0⟩ in the coordinate representation. A new operator's disentangling formula is derived as a by-product.

Quantum circuits for amplification of Kerr nonlinearity via quadrature squeezing

Phase shifts induced by the Kerr effect are usually very small at the single-photon level. We propose two circuits for enhancing the cross-Kerr phase shift by applying one- and two-mode quadrature squeezing operators. Our results are based on the vector coherent state theory and can be implemented by physical operations satisfying the commutation relations for generators of the generalized special unitary group, SU(1,1). While the proposed methods could be useful for the realization of quantum optical entangling gates based on Kerr nonlinear media at the single-photon level, they also indicate a general alternative approach to enhance higher-order nonlinearities by applying lower-order nonlinear effects.

Generation of multimode squeeze operators and multipartite entangled states for continuous variables

A scheme is presented for generating unitarily multimode field squeezing, cluster entanglement, and Greenberger-Horne-Zeilinger (GHZ) entanglement via cavity quantum electrodynamics. Through a suitable laser system, we are able to engineer a squeeze field operator decoupled from the atomic degrees of freedom, yielding a large squeeze parameter proportional to the number of atoms. The physical mechanism is attributed to the multiple four-photon processes and the dispersive atom-cavity-field interaction in large detuning systems.

Fast Generation of Einstein–Podolsky–Rosen States for Two Cavity Modes with a Collection of Driven Atoms

We propose an efficient scheme for realizing two-mode squeezing for two cavity modes with an atomic ensemble trapped in the cavity and driven by two classical fields. Through a suitable choice of the driving classical fields, the evolution dynamics of the two cavity modes is decoupled with the atomic system and described by a two-mode squeezing operator. We show that a highly squeezed state can be obtained at the output even with a bad cavity. The required experimental techniques are within the scope of what can be obtained in the BEC-cavity setup.

Gates for one-way quantum computation based on Einstein-Podolsky-Rosen entanglement

Single-mode squeezing and Fourier transformation operations are two essential logical gates in continuous-variable quantum computation, which have been experimentally implemented by means of an optical four-mode cluster state. In this paper, we present a simpler and more efficient protocol based on the use of Einstein-Podolsky-Rosen two-mode entangled states to realize the same operations. The theoretical calculations and the experimental results demonstrate that the presented scheme not only decreases the requirement to the resource quantum states at the largest extent but also enhances significantly the squeezing degree and the fidelity of the resultant modes under an identical resource condition. That is because in our system the influence of the excess noises deriving from the imperfect squeezing of the resource states is degraded. The gate operations applying two-mode entanglement can be utilized as a basic element in a future quantum computer involving a large-scale cluster state.

Studying bi-partite entangled state representations via the integration over ket-bra operators in $\mathfrak{Q}$ -ordering or $\mathfrak{P}$ -ordering

For two particles’ relative position and total momentum we have introduced the entangled state representation |η〉, and its conjugate state |ξ〉. In this work, for the first time, we study them via the integration over ket-bra operators in \(\mathfrak{Q}\)-ordering or \(\mathfrak{P}\)-ordering, where \(\mathfrak{Q}\)-ordering means all Qs are to the left of all Ps and \(\mathfrak{P}\)-ordering means all Ps are to the left of all Qs. In this way we newly derive \(\mathfrak{P}\)-ordered (or \(\mathfrak{Q}\)-ordered) expansion formulas of the two-mode squeezing operator which can show the squeezing effect on both the two-mode coordinate and momentum eigenstates. This tells that not only the integration over ket-bra operators within normally ordered, but also within \(\mathfrak{P}\)-ordered (or \(\mathfrak{Q}\)-ordered) are feasible and useful in developing quantum mechanical representation and transformation theory.

Dirac multimode ket-bra operators’ $\mathfrak{Q}$ -ordered and $\mathfrak{P}$ -ordered integration theory and general squeezing operator

We develop quantum mechanical Dirac ket-bra operator’s integration theory in \(\mathfrak{Q}\)-ordering or \(\mathfrak{P}\)-ordering to multimode case, where \(\mathfrak{Q}\)-ordering means all Qs are to the left of all Ps and \(\mathfrak{P}\)-ordering means all Ps are to the left of all Qs. As their applications, we derive \(\mathfrak{Q}\)-ordered and \(\mathfrak{P}\)-ordered expansion formulas of multimode exponential operator \(e^{ - iP_l \Lambda _{lk} Q_k } \). Application of the new formula in finding new general squeezing operators is demonstrated. The general exponential operator for coordinate representation transformation \(\left| {\left. {\left( {_{q_2 }^{q_1 } } \right)} \right\rangle \to } \right|\left. {\left( {_{CD}^{AB} } \right)\left( {_{q_2 }^{q_1 } } \right)} \right\rangle \) is also derived. In this way, much more correpondence relations between classical coordinate transformations and their quantum mechanical images can be revealed.

Detaching two single-mode squeezing operators from the two-mode squeezing operator

It has been common knowledge that the single-mode squeezing operator and the two-mode squeezing operator are independent of each other. However, in this work we find that after using the technique of integration within \U0001d514-ordering and \U0001d513-ordering, we can detach two single-mode squeezing operators from the two-mode squeezing operator. In other words, we show that the two-mode squeezing operator can be split into a \U0001d513-ordered two-mode squeezing operator (with a new squeezing parameter) and two single-mode squeezing operators (with another squeezing parameter). This tells us that the two-mode squeezing mechanism also involves some single-mode squeezing.

New entangled state representation and its characteristics for the three compatible operators

The eigenvector set of |φ(x, r 1, r 2)〉 with three compatible operators (\(\hat x_1 + \hat x_2 + \hat x_3\), \(\hat p_2 + \hat p_3 - 2\hat p_1\) and \(\hat p_3 - \hat p_2\)) is constructed by virtue of Radon transformation of the Wigner operator and the technique of integration within an ordered product (IWOP) of operators. Its entanglement property is then revealed by deriving its standard Schmidt decomposition. |φ(x, r 1, r 2)〉 makes up a new quantum mechanical representation. A new three-mode squeezing operator is found by using this entangled state representation.

Generalized coherent, squeezed and intelligent states for exactly solvable quantum systems and the analogue of the displacement and squeezing operators

Using an algebraic approach, we construct purely coherent and squeezed states for a set of exactly solvable quantum confined systems assuming a generalization of both the ladder-operator and the displacement-operator methods, showing the equivalence between the two procedures. We obtain the analogue of the displacement and the squeeze operators and study their basic relations and their connections with the properties of the purely coherent and squeezed states that they produce. In a second approach, we construct generalized squeezed coherent and intelligent states for these systems considering the successive action of the displacement and the squeeze operators (in the first case) and the combined action of these operators (in the second case). We apply the generalized approach for shape-invariant systems with potential parameters related by a translation and by a scaling and show that the presence of the generalizing functionals of the potential parameters in the formalism opens a large number of possibilities in the construction of these special quantum states.

Description of a domain using a squeezed state in a scalar field theory

We attempt to describe a domain using a squeezed state within quantum field theory. An extended squeeze operator is used to construct the state. Using a scalar field theory, we describe a domain in which the distributions of the condensate and of the fluctuation are both Gaussian. The momentum distribution, chaoticity, and correlation length are calculated. It is found that the typical value for the momentum is approximately the inverse of the domain size. It is also found that the chaoticity reflects the ratio of the size of the squeezed region to that of the coherent region. The results indicate that the quantum state of a domain is defined by these quantities under the assumption that the distributions are Gaussian. As an example, this method is applied to a pion field, and the momentum distribution and chaoticity are shown.

$\mathfrak{Q}$ -, $\mathfrak{P}$ -, and Weyl-ordering of Squeezing Operators: New Operator Identities and Applications

The basic operator ordering regarding to coordinate-momentum operator is discussed by virtue of the technique of integration within \(\mathfrak{Q}\)-ordering (all Q are on the left of all P) and \(\mathfrak{P}\)-ordering (all P are on the left of all Q). We derive new operator-ordering identities about \(\mathfrak{Q}\)-ordering , \(\mathfrak{P}\)-ordering and Weyl-ordering of both single-mode and two-mode squeezing operators. Its application in combinatorics is pointed out.

New Parameterized Coherent-Entangled State Representation and Its Applications

Based on EPR’s idea of quantum entanglement, new parameterized coherent-entangled states |α,p〉 μ,ν are introduced in two-mode Fock space, which can be implemented by using a beam splitter. Possible superpositions of |α,p〉 μ,ν result in some new entangled states. The asymmetric ket-bra integration from |α,p〉 μ,ν leads to a new one- and two-mode combinatorial squeezing operator with stronger squeezing, which clearly shows the intrinsic relationship between squeezing mechanism and quantum entanglement.

Light-Workover Cementing Technique Extends Life of Mature Indonesian Field

This article, written by Editorial Manager Adam Wilson, contains highlights of paper SPE 142827, ’Extending the Life of Mature Field by Light-Workover Cementing Technique,’ by Farid Hadiaman, SPE, Total, and Nilo Bianchi Neto, Schlumberger, prepared for the 2011 SPE Asia Pacific Oil and Gas Conference and Exhibition, Jakarta, 20-22 September. The paper has not been peer reviewed. Light-workover operations (LWOs) are well interventions performed without pulling out or replacing the completion of the well. Extensive LWOs are required to maintain satisfactory production at the mature Handil field in Indonesia. Among the LWOs executed in the field, a wide squeeze-cementing campaign was applied. These LWOs are used to isolate water-producing zones and target prospective new reservoir sections. For the Handil field, a field study analysis led to improved workover intervention with an alternative cement placement technique. Introduction Handil field is a giant mature oil field at the Mahakam delta, Indonesia (Fig. 1). It has been producing since 1975, with current recovery factors of 49% for oil and 57% for gas. Cumulatively, the total oil produced is approximately 855 million STB and total gas produced is approximately 1.68 Tcf. Currently, oil is being produced at 20,000 BOPD, gas at 75 MMscf/D, and water at 130,000 BWPD. Field Study Analysis Handil is composed of small stacked reservoirs with peculiar properties along its multizone completion. In order to allow selective production from different zones, 75% of the wells have dual-string completion (Fig. 2). Some wells had been water-flooded, and others have different types of casing damage. Thus, most of the challenges are related not only to the reservoir itself but also to dealing with parted tubing and with completion and packer leaking. Squeeze-cementing jobs are unique and challenging. Each job has to be specially analyzed and requires fit-for-purpose treatments. These jobs rely on multidisciplinary technology, requiring knowledge and skills in geomechanics, fluid mechanics, and, of course, cement/slurry systems. After decades of field and laboratory studies, when compared with primary cementing, squeeze cementing defies standardization as a general practice. Technical Aspects. Similar treatments used to be applied for different well conditions. No tailored cement systems or slurry properties were proposed on the basis of completion conditions, placement methodology, and injectivity results. The following are some improvement points that were identified. One Unique Job Design for Most of the Squeeze Treatments. A range of different design/execution possibilities was created on the basis of the injectivity test results. Different slurry recipes were prepared such that, if either low-, mid-, or high-injectivity results were encountered during the field test, the well would still be treated by a tailored slurry design. High fluid loss with higher rheology is now designed for higher injectivity results. Lower fluid loss and thin slurries are used for lower injection rates. Thickening Time Testing Schedule. A new thickening time schedule was implemented. For squeeze operation, the thickening time schedule should follow what is happening in the field as closely as possible.

Squeeze-swapping by Bell measurement studied in terms of the entangled state representation

By virtue of the entangled state representation (Hong-Yi Fan and J R Klauder 1994 Phys. Rev. A 49 704) and the two-mode squeezing operator's natural representation (Hong-Yi Fan and Yue Fan 1996 Phys. Rev. A 54 958) we propose the squeeze-swapping mechanism which can generate quantum entanglement and new squeezed states of continuum variables.

Wigner Function of the Two-Mode Squeezing-Enhanced Vacuum State

We find the two-mode generalized squeezing operator with two parameters can be separated into the product of a ordinary squeezing operator S2(ξ) and a rotating operator R2(θ). Acting it on the two-mode vacuum state, one can get two-mode squeezing-enhanced vacuum state (TSEVS). Compared with the usual two-mode squeezed vacuum state, TSEVS exhibits stronger squeezing properties. With the help of the operator’s Weyl-ordering invariance under the similarity transformation, we derive the Wigner function of the TSEVS.

Correspondence between quantum-optical transform and classical-optical transform explored by developing Dirac’s symbolic method

By virtue of the new technique of performing integration over Dirac’s ket-bra operators, we explore quantum optical version of classical optical transformations such as optical Fresnel transform, Hankel transform, fractional Fourier transform, Wigner transform, wavelet transform and Fresnel-Hadmard combinatorial transform etc. In this way one may gain benefit for developing classical optics theory from the research in quantum optics, or vice-versa. We cannot only find some new quantum mechanical unitary operators which correspond to the known optical transformations, deriving a new theorem for calculating quantum tomogram of density operators, but also can reveal some new classical optical transformations. For examples, we find the generalized Fresnel operator (GFO) to correspond to the generalized Fresnel transform (GFT) in classical optics. We derive GFO’s normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in the context of quantum optics. Especially, the introduction of quantum mechanical entangled state representations opens up a new area in finding new classical optical transformations. The complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Throughout our discussions, the coherent state, the entangled state representation of the two-mode squeezing operators and the technique of integration within an ordered product (IWOP) of operators are fully used. All these have confirmed Dirac’s assertion: “...for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory”.