УSpacetime and SubstanceФ, v.2, p.44, 2001

 

Cosmic maser as a remote quantum detector of the gravitational waves: on the possibilities of the OMPR-based method

 

Sergey Siparov

 

Department of Physics, Academy of Civil Aviation, 38 Pilotov St., St.Petersburg, 196210, Russia

 

 

Abstract

 

A new method based on the phenomenon of the optical-mechanical parametric resonance is proposed to detect the gravitational waves. The atoms and molecules responsible for the radiation of the cosmic masers can be described in frames of the two-level system model. The distance between these atoms and the Earth oscillates when the gravitational wave falls upon them. This affects the observable maser spectrum and a low frequency nonstationary component appears on it. The frequency of this component corresponds to the frequency of the gravitational wave. The needed astronomical observations and the additional instrumentation are described.

 

PACS number(s): 04.80.Nn, 95.75.St, 95.90.+v, 42.50.Vk

 

Introduction

 

This paper presents not a new result but rather a new idea based on the recently theoretically discovered effect of the optical-mechanical parametric resonance (OMPR) [1], [2]. The essence of it is that under special conditions the mechanical motion of atoms driven by a strong electromagnetic (EM) field essentially affects the observable spectrum. In case the atoms take part in the periodical motion (oscillate), a nonstationary component with large amplitude appears on the spectrum. Such a situation might take place when a gravitational wave (GW) produced by a periodical source passes through a cosmic maser whose signal is observed from the Earth. In spite of the fact that there is a number of serious questions that still remains, the discussion of the idea to regard a cosmic maser as a part of an instrument -- remote quantum detector -- to observe the GW with the help of specially modified radiotelescope might be of interest to the researchers.

Cosmic masers are the interstellar clouds where the concentrations of atoms are higher than the average. The atoms in these clouds may be excited by various external sources and emit the microwave radiation. Due to stimulated transitions (maser effect) the radiation is highly monochromatic, and its intensity grows as the radiation passes through the cloud. These regions are well observed from the Earth, their typical brightness temperatures being 10⁸ Ц 10¹² K, which corresponds to the flux density of 10² Ц 10⁴ Jy. The theory and experimental data for these objects are discussed in [3], [4].

Briefly speaking, the OMPR constitutes the following. Take a gas consisting of the two-level atoms (TLA), and let the strong resonant EM radiation pass through this gas. Use some periodical external source to bring the atoms into simultaneous mechanical oscillations (in laboratory frame) in parallel to the radiation beam. Let us assume that a) there is a non-zero

detuning of the EM radiation frequency Ω from the frequency of the atomic transition ω, b) the amplitude of the atomic mechanical oscillations suffices the amplitude condition

аааааааааааа аааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааааа(1)

here k is the wave vector of the electromagnetic field, V is the atomic velocity due to oscillations, аis Rabi parameter (or Rabi frequency), E is the electric component of the field, d is the

dipole moment of the atom, Ю is Planck's constant, ε is a small dimensionless parameter), and c) the frequency of the mechanical oscillations, D, suffices the tuning (or parametric resonance) condition

ааааааааааааааааааааааааааааааааааааааааааааааа аааааааааааааааааааааааааааааааааааааа(2)

(here V₀ is the thermal velocity of an atom). These conditions sufficed, the observable spectrum (absorption or radiation) essentially deforms and obtains a characteristic nonstationary feature, the amplitude of which is much larger than the height of the stationary resonant peak. 'Nonstationary' means that the absorption coefficient will have an additional component, the amplitude of which is a cosine function of time. This amplitude obtains both positive and negative values. Negative values in absorption correspond to the amplification, and, therefore, the mean (averaged over time) signal will be absent, because the amplification during one half of a period compensates the absorption during the other half of a period. But if the observation is performed with the help of an additional device like a lock-in amplifier, it is possible to register a signal at the frequency equal to the frequency of oscillations (and, as it was shown, it will be essentially higher than the regular stationary signal at the resonance frequency).

The curvature waves produced by a GW source act both on the Earth and on cosmic maser and lead to the varying of the separation between the Earth and maser's atoms, i.e. the distance between the atoms and the Earth oscillates. This is similar to what can take place in the laboratory investigations of the OMPR, when the distance between the (vibrating) atoms and the detector oscillates. Provided the OMPR conditions are fulfilled and the observation of maser radiation is modified in an appropriate way, the effect of the GW action could be registered, thus, giving the direct evidence of the GW existence. The sensitivity of the instruments now in use is sufficient to perform the measurements in question, since the stationary maser signals are easily detected by the existing radiotelescopes and the expected signal is larger than the signals already observed.

Unfortunately, this does not mean that the problem of the GW detection could be, thus, easily solved. Though technical problems of the instrument's sensitivity and noise filtration practically vanish, a purely astronomical and in a sense astrophysical problem of the search of the suitable maser arises. Nevertheless, it seems that the discussion of the applicability of the new principle to the solution of one of the most challenging problems of modern physics could be useful.

 

Detection of the gravitational waves

 

To apply the ideas supporting the OMPR effect to the GW detection with the help of the cosmic masers one has to check up three groups of assumptions:

(i) the physical backup: a) there must be a gas of the TLAs and a resonant monochromatic field that is strong in the spectroscopical sense, i.e. its Rabi parameter, α is larger than the TLA's excited state decay rate, γ, b) there must be a source that provides the oscillatory motion of the TLAs;

(ii) the OMPR conditions: a) Rabi frequency must be of the same order as the frequency of theа atoms oscillations; b) the amplitude of the oscillations must provide the possibility of the effect;

(iii) the observation possibilities: a) the relative location of the GW source, the maser and the observer; b) the instrument's sensitivity.

 

Physical backup

 

There is a number of various masers [5], [6] in space functioning in some of the regions where the concentrations of H, OH, H₂O, SiO and other atoms and molecules are higher than the average. The spectrum peaks corresponding to the radiation from these objects have the radio frequency and the line widths of such masers are usually about 10³ s^-1 . All these atoms and molecules in our case can be described in frames of the two-level system model (and will be called TLAs). If there is a pumping mechanism, the medium with the inverse population occurs. Two types of space masers are known: unsaturated and saturated, the latter being the one where the field is strong in the spectroscopical sense. The important thing is that in the saturated maser the intensity of radiation grows linearly [5] while propagating through the maser. The star shells also present suitable regions for space masers that could be of interest in view of our goal.

A rotating astrophysical object with the nonzero quadrupole moment can be a source of the tensor GW and a radially pulsating object -- a source of scalar GW. In this paper we will concentrate upon the periodical sources such as rotating neutron stars (e.g. the pulsar PSR 0532 in Crab nebulae). In this case the GW-source is highly monochromatic [7]. A GW produced by a source causes the varying of the distance between any two points with the frequency, D, equal to that of the GW. When the mechanical oscillations of atoms take place in a laboratory set up, the distance between the atoms and the detector (that presents the laboratory reference frame), also changes in the similar manner. It is this effect that can lead to the OMPR in the laboratory, and this is why it is possible to apply the OMPR for the search of the GW with the help of cosmic masers.

The intensity of the driving EM field interacting with the atom is characterized by Rabi parameter (or Rabi frequency) . The СstrongТ field means that the stimulated

absorption-emission governs the atomic behavior, i.e. γ/α = ε where εа is small. In view of our goal and with regard to the OMPR conditions discussed further, α must be of the same order as D -- the frequency of the mechanical oscillations. The GW frequencies vary from 10¹ s^-1 for the periodical sources (e.g. pulsar in the Crab nebulae) to 10³ s^-1 corresponding to the catastrophic events in the Galaxy nucleus [8], [9]. Let a periodical source have frequency proportional to 10¹ s^-1. Then, if we assume ε ~ 0.01, the value of the excited state decay rate γ corresponding to the strong field should be of the order of 10^-1 s^-1а i.e. the excited state of the atom is metastable. In [10] it was found that the OH-radical has a suitable rotational transition (its frequency [11] is of the order of 10⁹ Ц 10¹⁰ s^-1 with γа ~ 10^-1 s^-1 . In [10] this value was used to evaluate the OH space maser dimensions. The intensity of the radio signal coming to the Earth from a typical OH-maser corresponds to the intensity I at the maser border equal to 10²² W , while a typical maser dimension r_m has a value ofа 10¹² m. To evaluate the electric stress of the field at the maser border E_m , the formulas for the power flow аand а(ε₀а = 8.85*10^-12а F/m -- absolute dielectric permittivity) can be used, and the stress appears to be about E_m = 10⁰ V/m. Substituting this value into the formula for Rabi frequency, we see that in the depth of the maser cloud there is a region with α ~ 10¹ s^-1 providing the chosen value ε ~ 10^-2. And the OH maser sources are frequent in space.

Thus, there are regions in space where there exist the two-level atoms driven by a strong resonant monochromatic field (e.g. OH-masers), and there exist the external sources (e.g. pulsars) that can ''make these atoms oscillate'' with regard to the Earth location when the GW passes through the maser.

 

OMPR conditions

 

The OMPR conditions a), b) (eq.1) and c) (eq.2) mentioned in the Introduction were obtained in [1], [2].

A non-zero detuning of the radiation frequency from the frequency of the atomic transition can be delivered by the consideration of the non-zero velocity of the interstellar gas leading to the Doppler shift of the resonance frequency.

Let us now evaluate the needed amplitude of the atoms' oscillations providing the OMPR. Substituting аinto eq.1, we find that the vibrating maser's atom must have the amplitude of vibration equal to A^-4m. This value of the amplitude can cause the effect in the case under discussion. The possibility to have this value for maser observations is discussed in the next subsection.

To suffice the resonance condition, the GW frequency must be proportional to the maser radiation intensity, and D ~ α. But the maser diameter is very large, and the radiation intensity varies while propagating through the maser. Thus, the precise tuning for the given frequency of external action -- that is the expected GW frequency -- can be reached only in the region of a maser where Rabi frequency suffices the OMPR condition. For other maser's parts located further and nearer to the observer, this condition would be broken. But the existence of an OMPR-region, even though it is just a part of a maser as a whole, could be enough to provide the main thing -- that is the appearance of the nonstationary component in the spectrum. Observed with the help of an additional device like a low frequency lock-in (LFL), it would point at the OMPR caused by the atoms' oscillation. Other effects like weak field resonance fluorescence, or Doppler driven spectral changes would not count in the nonstationary component of the signal. There is a possibility that the amplitude of the observable nonstationary signal would not be higher than the value of the stationary signal already observable. This can happen in the case when the maser OMPR-region is far from the closest to the Earth maser ''border'' . Still, the hope remains to recognize the existence of the OMPR caused by the gravitational radiation with the help of an LFL and observe only the low frequency GW-modulated part of the maser signal.

Let us now evaluate the longitudinal and transversal dimensions of the OMPR-region with regard to the observation line (OL). Considering the spatial extent of the cosmic maser, the attention should be paid to the following: a) could the EM radiation propagating through the maser and along the OL consequently meet atoms with counterphase displacements with regard to the Earth, that will, thus, destroy the effect?; b) could the EM radiation from the points that are situated at half a GW wavelength from one another along the GW wave vector (i.e. perpendicular to the OL) be self compensating when being registered by an instrument on the Earth? Question b) deals with the angular resolution of existing instruments. The point of observation must have the angular dimension that is less than half of the GW wave length, which is equal to cD and in our case is aboutа 10⁶ m. This is within the resolution possibilities of the modern radiotelescopes. Question a) is more complicated and demands the following analysis. One has to estimate the longitudinal dimension of the region where the OMPR conditions are fulfilled, and make sure that it is not larger than the half of the GW length. Since E² grows linearly while the EM radiation propagates through the maser, we can estimate the distance passed by the radiation until the OMPR tuning condition is broken. Let E_m² correspond to the maser border (i.e. to the observable stationary signal), r_mа is maser dimension, E_R² is the field needed to provide the value of Rabi frequency sufficing the tuning condition, r is the distance between the mase's border (furthermost from the observer) and the region where the OMPR could take place. When the radiation reaches r + Δr point, the intensity becomes proportional to (E_R + ΔE)². The linear increase of the intensity in the saturated masers leads to the simple proportions (r+Δr)/r = (E_R + ΔE)²/E_R² and r / E_R² = r_m /E_m² , which give Δr = 2(E_R ΔE/E_m²)r_m . The electric component E_R is proportional to Rabi frequency α , and if the parametric resonance tuning Δα is chosen to be equal to εα, then ΔE will be equal to εE_R. Thus, for the longitudinal dimension of the OMPR region one gets

ааааааааааааааааааааааааааааааааааааааааааааа ааааааааааааааааааааааааааааааааааааааааааааааааааа(3)

For the typical OH-masers the squared electric stress at the border is E_m² = 10⁰ V² /m². In the definition аone should choose α = 10¹ s^-1 , the dipole moment is [12] d = 6 * 10^-30 C*m, then in the OMPR region of the maser аV²/m² . Substituting these values into eq.3, one gets Δrа = 10⁵m. If the maser intensity is larger than the mentioned typical value, then the OMPR region is more compact, and the possibility to suffice the tuning condition increases. Note, that simultaneously the number of atoms taking part in the effect decreases, and higher density of the cloud is needed. If the maser intensity is less than the given value, the OMPR region increases, and the atoms separated by the distance larger than the GW length move in the counterphase and can destroy the effect. Thus, the OMPR conditions can be fulfilled, but a suitable maser must be carefully selected.

 

Observation possibilities

 

Now let's investigate the possibilities for the maser location to meet the needed value of the amplitude. The metric tensor component h = | h_αβ | corresponding to the gravity radiation emitted by an object like a neutron star is inversely proportional to the distance from the source, and is equal [7], [13] to

ааааааааааааааааааааааааааааааааааааааааа ааааааааааааааааааааааааааааааааааааааааааааа(4)

where G is the gravitation constant; M is the star mass; L is the star linear dimension; r is the distance to the region where the GW acts on a detector (here: on a TLA in a maser), g_e is the gravitational ellipticity in the equatorial plane of a star.

The free bodies methods of the GW detection take into account the relation l₁ / l = 1/2h, where l is the distance between the two free bodies at small separation in the flat space (interferometer mirrors), and l₁ is the variation of this distance due to curvature waves [8]. The value of l₁ will reach its maximum for the local detector, when l (the interferometer arm) is equal to the half of the GW length. In all the other cases, be l several times less or larger than this value, the situation won't improve because the value of h for the local detector remains the same. But for the remote quantum detector the situation is different. One of the two free bodies in question (here: OMPR region of a maser) can be located in a region where h is essentially larger, i.e. in the vicinity of the star (GW source). The most favorable position for the maser is on the circle, the diameter of which connects the Earth and the GW source. In this case the distance between the (tensor) GW source and the Earth does not variate due to this source's gravity radiation, while the maser-to-Earth distance variates in the maximal way. To enlarge the amplitude of the maser's atom oscillations (in the Earth reference frame), the maser should be close to the GW source.

Let us evaluate the distance from the GW source to a place, where the displacement l₁ of the maser's atoms suits the OMPR amplitude condition A = 10^-4 m obtained in the previous subsection. To do this let us pretend that we deal with the local detector, and its interferometer arm is equal to the half of the GW length, i.e. l ~ 10⁶ m. Then for l₁ ~ 10^-4 m, the formula l₁ / l = 1/2h gives h ~ 10^-8 which is enormous in comparison to its value on the Earth but is reasonable for the star vicinity. Notice, that this value is still small enough to be within the assumptions of the weak field general relativity approach. Substituting this value of h and, e.g., Crab pulsar's characteristics M = 2.4*10³⁰ kg, L = 1.2*10⁴ m, D = 63 Hz ~ 400 s^-1 , into eq.4 and taking [13] g_e = 6*10^-4 , we obtain r ~ 10⁵m . This is just below the border of the wave zone for the Crab GW source. If we consider Vela pulsar that has the similar values for mass and dimension [14] but has D = 22 Hz and g_e = 4*10^-3 [13], we get the same order of the distance in question r ~ 10⁵ m. The gravitational ellipticity factor could play an essential role in the estimation of r, but the known values for it vary in different papers (e.g. in the earlier work [15] there were g_e = 3*10^-6 for Crab and g_e = 3*10^-5 for Vela, both of which are worse in view of our goal). This means that the search for the GW source has the additional restriction due to the gravitational ellipticity factor.

Now let us drag one of the mirrors of our interferometer as far as the Earth. In view of the ''interferometric'' observational possibilities, this will not change the experimental situation significantly. Notice also, that as we saw in the previous subsection, the dimensions of the OMPR maser region is comparable to the GW length. This means that the neighboring maxima and minima of the GW will not compensate each other when driving the atoms.

The chance of an astronomical maser being located within the due distance from a suitable rotating and distorted neutron star is rather low, but as it was already mentioned earlier the star shells can also reveal maser properties. In [16], [17] there are some examples of the atmospheres around neutron stars in X-ray binaries, though the atmospheres discussed there are far different from those that could support an astrophysical maser. Particularly, the soft X-ray thermal radiation field would completely dissociate any of the molecules required for an astrophysical maser. This last problem can be avoided by assuming a single neutron star that has cooled to a very low surface temperature, if that can occur in a Hubble time.

The density of the maser region must be high enough to provide the sufficient number of atoms taking part in the OMPR. Let there be 10 atoms on every linear centimeter of the OMPR maser region along the observation line. Then for Δrа ~ 10⁵ m there will be 10⁸ atoms, which is a

detectable number of atoms even for a regular experiment in which the stationary component is registered.

The conclusion is that the suitable maser must be located in a star vicinity. In this case the corresponding observations in search for the GW with the help of OMPR will be possible. The sensitivity of the existing instruments able to measure the regular maser signal is enough to observe the high nonstationary peak. This means that the signal-to-noise ratio will not be a problem when the suggested method is used.

 

Discussion

 

The method discussed in this paper differs from the known methods [18] and suggests a direct observation of GW in contrast to that of [19]. It is based on the new principle which is the registration of the OMPR in cosmic masers. As it follows from the reasoning given above, the sensitivity of the already existing astrophysical instruments is enough to detect the effect if any. Thus, the problem in question changes: from a purely technical struggle for the high sensitivity it becomes an astronomical search for a suitable maser.

The following plan of the experiment can be proposed. The radio telescope is fixed at the suitable TLA transition of the selected space maser. The maser signal registered by a radiotelescope is processed by an additional low frequency lock-in amplifier. Simultaneously, the lock-in is synchronized with a reference strobe signal from the low frequency generator working at 10¹ Ц10³ s^-1. The search at the frequencies corresponding to the periodical GW sources is to be performed. In case the conditions of the OMPR are fulfilled the low frequency peak will appear and present a proof of the GW existence. This signal can be distinguished from the others because it reveals itself in the nonstationary component of the signal.

In conclusion it should be underlined once again that this paper is devoted to the discussion of the new method of the GW detection. Instead of dealing with the technical difficulties in the Earth laboratories, we confront the problem of the search for the suitable cosmic maser which is not that easy. As it was shown, the needed astrophysical conditions are at the limit of the method's applicability. The discussed approach gives a new direction of thought for the problem of the gravitational waves detection.

 

Bibliography

 

[1] Siparov S.V., Phys.Rev.A, 55, 3704 (1997)

 

[2] Siparov S.V., J.Phys.B,а 31, 415 (1998)

 

[3] Cook A.H., Celestial masers, Cambridge University Press, London (1977)

 

[4] Elitzur M., Astronomical masers, Kluwer Academic Publishers, Boston1992

 

[5]а Bochkarev N.G., Osnovy fiziki mejzvezdnoi sredy (The Basic Physics of the Interstellar Media), Moscow State University Publ., Moscow (1992)

 

[6]а Zeldovich Ya.B., Novikov I.D., Fizika mejzvezdnoi sredy (Physics of the Interstellar Medium), Nauka, Moscow (1988)

 

[7]а Bicak J., Rudenko V.N., Gravitatsionnye volny v OTO i problema ih obnarujeniia (Gravitational waves in GRT and the problem of their detection, Moscow State University, Moscow (1987)

 

[8]а Amaldi E., Pizzella G., in Astrofisika e Cosmologia Gravitazione Quanti e Relativita, Guinti Barbera, Firenze, (Rus.trans. Mir, Moscow (1982), p.241) (1979).

 

[9]а Rees M., Ruffini R., Wheeler J., Black Holes, Gravitational Waves and Cosmology. (Rus.trans. Mir, Moscow, 1977)

 

[10] Goldreich P., Keely D.A., Astophys.J, 174, 515 (1972)

 

[11] Litvak M.M., in Atoms and Molecules in Astrophysics, Academic Press, London and New York (1972)

 

[12] Radtsig A.A., Smirnov B.M., Parametry atomov i atomnyh ionov (Parameters of atoms and atomic ions), Energoizdat, Moscow (1986)

 

[13] Thorne K.S., in Three hundred years of gravitation, eds. Hawking S.W. and Israel W., Cambrifge University Press (1987).

 

[14] Link B, Epstein RI, Lattimer JM, Phys.Rev.Lett., 83, 3362 (1999)

 

[15]а Zimmermann M, Nature, 271, 524 (1978)

 

[16]а Heyl JS, Astrophys.J, 542, L45 (2000)

 

[17] Rutledge RE et al., Astrophys.J., 529, 985 (2000)

 

[18]а Schutz B.F., Class. Quantum Grav. 16, A131 (1999)

 

[19]а Hulse R.A., Taylor J.H., Astrophys J., 195, L-51 (1975)