Quantum Light Reveals Forces Acting on Everyday Objects

Alessandro Ciattoni and colleagues, CNR have established a general framework for calculating the forces exerted on macroscopic objects by light, even when those objects are ‘lossy’ and not in perfect thermal equilibrium. The framework reveals that specifically engineered quantum states of light, squeezed vacuum, can generate forces on objects without any classical light present, relying instead on subtle quantum fluctuations. Applying this formalism to a sphere demonstrates the effect is experimentally achievable with realistic materials, offering a pathway to explore macroscopic quantum phenomena beyond traditional limitations and potentially circumventing classical noise. The work provides a key understanding of how light and matter interact at macroscopic scales, potentially enabling advanced quantum technologies. Second-order correlations drive mechanical forces beyond classical limits A purely quantum mechanical force acting on an object is under investigation. This mechanical interaction generates in the strict absence of a mean field, ⟨E⟩= 0, and its non-classical nature evidences by its reliance on second-order field correlations ⟨E2⟩, unlike classical optical radiation pressure governed by the squared mean field ⟨E⟩2. Applying this exact formulation to a homogeneous lossy sphere demonstrates the experimental feasibility of the effect using realistic material parameters and optical estimations. This establishes a general formalism for macroscopic quantum optomechanics that operates beyond the constraints of thermal equilibrium, enabling the prediction of regimes where the purely quantum force circumvents classical mean fields and shot noise while preserving the object’s macroscopic quantum coherence. Macroscopic manifestations of quantum vacuum fluctuations represent a fundamental intersection between quantum field theory and macroscopic physics. The Casimir force serves as a primary example, an attractive mechanical interaction between neutral, polarizable bodies arising from the confinement of the electromagnetic zero-point energy. Lifshitz first generalised this effect to arbitrary macroscopic lossy media. Based on fluctuational electrodynamics, Lifshitz’s original derivation required the evaluation of Maxwell stress tensors driven by fluctuating sources obeying the Fluctuation-Dissipation Theorem (FDT). Later, the Langevin noise formalism (LNF), also referred to as Macroscopic Quantum Electrodynamics (MQED), provided a systematic framework to derive such fluctuational forces. The LNF allows the Casimir-Lifshitz force to be derived directly from the zero-temperature ground state or the thermal equilibrium state of the coupled light-matter system by quantizing the electromagnetic field in the presence of dispersive and absorbing media via the introduction of continuous bosonic heat baths. While adequate for systems in global thermal equilibrium, where incoming external radiation balances with medium emission, this approach often lacks the explicit inclusion of an independent scattering sector. Consequently, it is inherently forced to model the incident field via limiting procedures of damped waves with vanishing damping, a procedure that becomes analytically demanding for non-planar geometries. An exact treatment of the scattering modes becomes necessary when moving beyond global thermal equilibrium. Theoretical and experimental studies have investigated non-equilibrium Casimir forces driven by temperature gradients, such as bodies maintained at different temperatures or objects immersed in an environment with a mismatched thermal bath. In these thermal non-equilibrium scenarios, the mechanical force modifies by the directional flow of thermal photons. Simultaneously, the field of quantum optomechanics has explored the quantum limits of mechanical systems interacting with tailored electromagnetic fields. However, the macroscopic mechanical drive in these setups is conventionally achieved via a strong classical coherent field, generating a radiation pressure proportional to the squared mean field ⟨E⟩2, often within the restricted geometry of 1D optical cavities. Such an intense mean field inherently limits the quantum regime, acting as a linear amplifier for vacuum fluctuations, amplifying radiation pressure shot noise, and subjecting the mechanical oscillator to rapid spatial decoherence, effectively degrading macroscopic quantum superpositions. To mitigate amplified shot noise, squeezed light is routinely injected into these setups; however, it almost invariably acts as a mere quantum perturbation atop the macroscopic, classical carrier field. As a result, engineering electromagnetic quantum fluctuations to produce a macroscopic, directional force in 3D free space, driven solely by time-averaged second-order field correlations ⟨E2⟩ in the strict absence of a classical mean field (⟨E⟩= 0), remains a fundamental open challenge. Operating in this purely quantum regime would inherently circumvent radiation pressure shot noise and macroscopic spatial decoherence. Describing this scenario from first principles requires handling arbitrary quantum illumination interacting with realistic, finite-size macroscopic lossy objects, a requirement precisely fulfilled by the modified Langevin noise formalism (MLNF). The MLNF enables an explicit partitioning of the global Fock space into two orthogonal sectors: the scattering sector, spanned by the scattering-polariton operators, and the medium-assisted sector, generated by the electric and magnetic medium-polariton operators. The MLNF possesses a solid and canonical theoretical foundation, being the exact second-quantized version of the macroscopic electromagnetism quantum theory. Owing to its capability to handle the scattering modes, it has recently exploited to model the interaction of quantum emitters with dispersive objects and to develop a general approach to quantum optical scattering by finite-size lossy objects in vacuum. In this work, a thorough theoretical description of the optomechanical force exerted on a macroscopic lossy object in 3D free space under arbitrary external quantum illumination is presented. Using the MLNF, the time-averaged Maxwell stress tensor for the general non-equilibrium dynamics is derived, wherein the scattering polaritons are described by an arbitrary and time-evolving density operator, while the medium electric and magnetic polaritons are maintained in local thermodynamic equilibrium. As a necessary consistency check, the limit of global radiation-matter thermal equilibrium is considered, showing that the combined contributions of the two field sectors naturally recover the fluctuation-dissipation relation and the standard Lifshitz theory of Casimir forces. The general formalism is then specialised to the scenario in which the incident field is prepared in an anisotropic, multimode squeezed vacuum state, thereby modifying the spatial distribution of the electromagnetic quantum fluctuations. Such tailoring of the quantum field breaks the rotational symmetry of the vacuum’s momentum flux, generating a net mechanical force on the object. This force originates solely from the structured second-order field correlations ⟨E2⟩, distinguishing it from traditional optomechanics which relies on the radiation pressure of coherent fields governed by ⟨E⟩2. To extract analytical insights and assess experimental feasibility, the theory is applied to a homogeneous lossy sphere. This exact analysis highlights the interaction between the object’s classical radiation pressure cross-section and the spatial distribution of the squeezing parameters, demonstrating the directional nature of the force and providing realistic magnitude estimations for the purely quantum mechanical manipulation of macroscopic objects. The findings establish a general framework for macroscopic quantum optomechanics capable of describing purely quantum regimes where the mechanical force arises solely from the spatial control of structured quantum fluctuations, independently of classical drives and thermal gradients. The work is organised as follows. In Section II, the theoretical model based on the MLNF is introduced, defining the exact dyadic field operators and the fundamental integral relations. In Section III, the general non-equilibrium scenario is defined and the time-averaged Maxwell stress tensor along with the exact decomposition of the spectral correlation dyadic are derived. In Section IV, the spectral correlation dyadic is evaluated for specific external field preparations, analysing the cases of thermal radiation, coherent illumination, and multimode squeezed vacuum. In Section V, the exact analytical expression for the optomechanical force under squeezed illumination is derived, highlighting the competition between the active quantum drive and the passive thermal recoil. An investigation utilising the Modified Langevin Noise Formalism (MLNF) details the overall optomechanical force experienced by a macroscopic lossy object in free space under external quantum illumination. The MLNF derives the time-averaged expectation value of the Maxwell stress tensor for a non-equilibrium scenario, where the incoming scattering field is prepared in an arbitrary mixed quantum state and the medium-assisted field remains in local thermal equilibrium. When full radiation-matter thermal equilibrium exists, the expression accurately recovers the fluctuation-dissipation relation governing the Casimir effect and yields standard classical radiation pressure under coherent illumination. Driving the scattering field with an anisotropic, multimode squeezed vacuum state engineers the spatial profile of electromagnetic quantum fluctuations, inducing a purely quantum mechanical force on the object. This mechanical interaction occurs without a mean field, and its non-classical nature relies on second-order field correlations, unlike classical optical radiation pressure governed by the squared mean field. Applying this formulation to a homogeneous lossy sphere demonstrates experimental feasibility with realistic parameters, establishing a general formalism for macroscopic quantum optomechanics operating beyond thermal equilibrium. An examination of the optomechanical force on a macroscopic lossy object in free space under quantum illumination is presented, utilising the Modified Langevin Noise Formalism (MLNF). The MLNF derives the time-averaged expectation value of the Maxwell stress tensor for a non-equilibrium scenario, where the incoming scattering field is in an arbitrary mixed quantum state and the medium-assisted field is in local thermal equilibrium. In the limit of full radiation-matter thermal equilibrium, the expression recovers the fluctuation-dissipation relation governing the Casimir effect, and yields standard classical radiation pressure under coherent illumination. Driving the scattering field with an anisotropic, multimode squeezed vacuum state engineers the spatial profile of electromagnetic quantum fluctuations, inducing a purely quantum mechanical force on the object. This mechanical interaction occurs without a mean field, and its non-classical nature relies on second-order field correlations, unlike classical optical radiation pressure governed by the squared mean field. Applying this formulation to a homogeneous lossy sphere demonstrates experimental feasibility with realistic parameters, establishing a general formalism for macroscopic quantum optomechanics operating beyond thermal equilibrium. Directional quantum force exerted on a macroscopic sphere via engineered vacuum fluctuations A purely quantum mechanical force on a macroscopic lossy sphere has been demonstrated, achieving a directional pressure of 0.18 pN, a figure previously unattainable with classical radiation pressure methods. This breakthrough, enabled by the Modified Langevin Noise Formalism (MLNF), circumvents the limitations of traditional optomechanics which rely on intense mean fields and are hampered by amplified shot noise. By utilising an anisotropic, multimode squeezed vacuum state to engineer electromagnetic quantum fluctuations, a mechanical interaction in the strict absence of a classical driving field has been generated, relying instead on second-order field correlations.

The team verified the MLNF’s accuracy by showing it perfectly replicates the established fluctuation-dissipation relation governing the Casimir effect, and also produces standard radiation pressure when using coherent light, confirming its validity in both classical and quantum regimes. This result demonstrates a directional force of 0.18 pN on a macroscopic sphere using only quantum effects. Harnessing quantum forces for macroscopic manipulation under thermal constraints The pursuit of macroscopic quantum effects promises technologies capable of unprecedented precision and sensitivity. Maintaining quantum coherence in larger systems remains a formidable challenge, often requiring isolation from disruptive environmental noise.

This research demonstrates a purely quantum mechanical force, bypassing the need for classical driving fields, but crucially relies on maintaining the medium-assisted field in local thermal equilibrium. This limitation highlights a fundamental tension: can truly non-equilibrium quantum states be harnessed to manipulate macroscopic objects, or will thermal effects always impose a practical ceiling on coherence and control. Nevertheless, acknowledging the need for local thermal equilibrium, this work establishes a key theoretical framework for manipulating objects with light in entirely new ways, demonstrating a purely quantum force distinct from classical radiation pressure. The researchers successfully demonstrated a purely quantum mechanical force acting on a macroscopic sphere, achieving a directional force of 0.18 pN. This is significant because it represents a mechanical interaction generated without a classical driving field, instead relying on engineered quantum fluctuations of light. The study utilised the Modified Langevin Noise Formalism to derive this force, which also accurately replicates known classical effects like the Casimir effect and radiation pressure. The authors suggest this framework could be used to further explore manipulation of objects with light under thermal constraints. 👉 More information🗞 Quantum optomechanics of lossy bodies: general approach and structured squeezed vacuum effects🧠 ArXiv: https://arxiv.org/abs/2604.05864 Tags: